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LIPIcs, Volume 358
20th International Symposium on Parameterized and Exact Computation (IPEC 2025)
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- published at: 2025-12-15
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-407-9
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Complete Volume
LIPIcs, Volume 358, IPEC 2025, Complete Volume
Abstract
LIPIcs, Volume 358, IPEC 2025, Complete Volume
Cite as
20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1-590, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@Proceedings{agrawal_et_al:LIPIcs.IPEC.2025,
title = {{LIPIcs, Volume 358, IPEC 2025, Complete Volume}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {1--590},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025},
URN = {urn:nbn:de:0030-drops-252604},
doi = {10.4230/LIPIcs.IPEC.2025},
annote = {Keywords: LIPIcs, Volume 358, IPEC 2025, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2025.0,
author = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {0:i--0:xviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.0},
URN = {urn:nbn:de:0030-drops-252591},
doi = {10.4230/LIPIcs.IPEC.2025.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)
Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
Cite as
Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
author = {Kouteck\'{y}, Martin},
title = {{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {1:1--1:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
URN = {urn:nbn:de:0030-drops-251338},
doi = {10.4230/LIPIcs.IPEC.2025.1},
annote = {Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
Directed Disjoint Paths Remains W[1]-Hard on Acyclic Digraphs Without Large Grid Minors
Abstract
In the Vertex-Disjoint-Paths-With-Congestion problem, the input consists of a digraph D, an integer c and k pairs of vertices (s_i, t_i), and the task is to find a set of paths connecting each s_i to its corresponding t_i, whereas each vertex of D appears in at most c many paths. The case where c = 1 is known to be NP-complete even if k = 2 [Fortune, Hopcroft and Wyllie, 1980] on general digraphs and is W[1]-hard with respect to k (excluding the possibility of an f(k)n^O(1)-time algorithm under standard assumptions) on acyclic digraphs [Slivkins, 2010]. The proof of [Slivkins, 2010] can also be adapted to show W[1]-hardness with respect to k for every congestion c ≥ 1.
We strengthen the existing hardness result by showing that the problem remains W[1]-hard for every congestion c ≥ 1 even if: (1) the input digraph D is acyclic, (2) D does not contain an acyclic (5, 5)-grid as a butterfly minor, (3) D does not contain an acyclic tournament on 9 vertices as a butterfly minor, and (4) D has ear-anonymity at most 5.
Further, we also show that the edge-congestion variant of the problem remains W[1]-hard for every congestion c ≥ 1 even if: (1) the input digraph D is acyclic, (2) D has maximum undirected degree 3, (3) D does not contain an acyclic (7, 7)-wall as a weak immersion and (4) D has ear-anonymity at most 5.
Cite as
Ken-ichi Kawarabayashi, Nicola Lorenz, Marcelo Garlet Milani, and Jacob Stegemann. Directed Disjoint Paths Remains W[1]-Hard on Acyclic Digraphs Without Large Grid Minors. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{kawarabayashi_et_al:LIPIcs.IPEC.2025.2,
author = {Kawarabayashi, Ken-ichi and Lorenz, Nicola and Garlet Milani, Marcelo and Stegemann, Jacob},
title = {{Directed Disjoint Paths Remains W\lbrack1\rbrack-Hard on Acyclic Digraphs Without Large Grid Minors}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {2:1--2:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.2},
URN = {urn:nbn:de:0030-drops-251347},
doi = {10.4230/LIPIcs.IPEC.2025.2},
annote = {Keywords: digraphs, parameterized complexity, disjoint paths, butterfly minors, immersions, ear anonymity}
}
Document
Parameterized Maximum Node-Disjoint Paths
Abstract
We revisit the Maximum Node-Disjoint Paths problem, the natural optimization version of the famous Node-Disjoint Paths problem, where we are given an undirected graph G, k (demand) pairs of vertices (s_i, t_i), and an integer 𝓁, and are asked whether there exist at least 𝓁 vertex-disjoint paths in G whose endpoints are given pairs. This problem has been intensely studied from both the approximation and parameterized complexity point of view and is notably known to be intractable by standard structural parameters, such as tree-depth, as well as the combined parameter 𝓁 plus pathwidth. We present several results improving and clarifying this state of the art, with an emphasis towards FPT approximation.
Our main positive contribution is to show that the problem’s intractability can be overcome using approximation: We show that for several of the structural parameters for which the problem is hard, most notably tree-depth, the problem admits an efficient FPT approximation scheme, returning a (1-ε)-approximate solution in time f(td,ε)n^𝒪(1). We manage to obtain these results by comprehensively mapping out the structural parameters for which the problem is FPT if 𝓁 is also a parameter, hence showing that understanding 𝓁 as a parameter is key to the problem’s approximability. This, in turn, is a problem we are able to solve via a surprisingly simple color-coding algorithm, which relies on identifying an insightful problem-specific variant of the natural parameter, namely the number of vertices used in the solution.
The results above are quite encouraging, as they indicate that in some situations where the problem does not admit an FPT algorithm, it is still solvable almost to optimality in FPT time. A natural question is whether the FPT approximation algorithm we devised for tree-depth can be extended to pathwidth. We resolve this negatively, showing that under the Parameterized Inapproximability Hypothesis no FPT approximation scheme for this parameter is possible, even in time f(pw,ε)n^g(ε). We thus precisely determine the parameter border where the problem transitions from "hard but approximable" to "inapproximable".
Lastly, we strengthen existing lower bounds by replacing W[1]-hardness by XNLP-completeness for parameter pathwidth, and improving the n^o(√{td}) ETH-based lower bound for tree-depth to (the optimal) n^o(td).
Cite as
Michael Lampis and Manolis Vasilakis. Parameterized Maximum Node-Disjoint Paths. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{lampis_et_al:LIPIcs.IPEC.2025.3,
author = {Lampis, Michael and Vasilakis, Manolis},
title = {{Parameterized Maximum Node-Disjoint Paths}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.3},
URN = {urn:nbn:de:0030-drops-251357},
doi = {10.4230/LIPIcs.IPEC.2025.3},
annote = {Keywords: ETH, Maximum Node-Disjoint Paths, Parameterized Complexity, PIH}
}
Document
On the Complexity of Secluded Path Problems
Abstract
This paper investigates the complexity of finding secluded paths in graphs. We focus on the Short Secluded Path problem and a natural new variant we introduce, Shortest Secluded Path. Formally, given an undirected graph G = (V, E), two vertices s,t ∈ V, and two integers k,l, the Short Secluded Path problem asks whether there exists an s-t path of length at most k with at most l neighbors. This problem is known to be computationally hard: it is W[1]-hard when parameterized by the path length k or by cliquewidth, and para-NP-complete when parameterized by the number l of neighbors. The fixed-parameter tractability is known for k+l or treewidth. In this paper, we expand the parameterized complexity landscape by designing (1) an XP algorithm parameterized by cliquewidth and (2) fixed-parameter algorithms parameterized by neighborhood diversity and twin cover number, respectively. As a byproduct, our results also provide parameterized algorithms for the classic s-t k-Path problem. Furthermore, we introduce the Shortest Secluded Path problem, which seeks a shortest s-t path with the minimum number of neighbors. In contrast to the hardness of the original problem, we reveal that this variant is solvable in polynomial time on unweighted graphs. We complete this by showing that for edge-weighted graphs, the problem becomes W[1]-hard yet remains in XP when parameterized by the shortest path distance between s and t.
Cite as
Tesshu Hanaka and Daisuke Tsuru. On the Complexity of Secluded Path Problems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hanaka_et_al:LIPIcs.IPEC.2025.4,
author = {Hanaka, Tesshu and Tsuru, Daisuke},
title = {{On the Complexity of Secluded Path Problems}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {4:1--4:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.4},
URN = {urn:nbn:de:0030-drops-251361},
doi = {10.4230/LIPIcs.IPEC.2025.4},
annote = {Keywords: Secluded path, Parameterized complexity, Polynomial-time algorithm}
}
Document
Kernelization for H-Coloring
Abstract
For a fixed graph H, the H-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of H. A seminal theorem of Hell and Nešetřil asserts that the H-Coloring problem is NP-hard whenever H is loopless and non-bipartite. A result of Jansen and Pieterse implies that for every graph H, the H-Coloring problem parameterized by the vertex cover number k admits a kernel with O(k^Δ(H)) vertices and bit-size bounded by O(k^Δ(H)⋅log k), where Δ(H) denotes the maximum degree in H. For the case where H is a complete graph on at least three vertices, this kernel size nearly matches conditional lower bounds established by Jansen and Kratsch and by Jansen and Pieterse.
This paper presents new upper and lower bounds on the kernel size of H-Coloring problems parameterized by the vertex cover number. The upper bounds arise from two kernelization algorithms. The first is purely combinatorial, and its size is governed by a structural quantity of the graph H, called the non-adjacency witness number. As applications, we obtain kernels whose size is bounded by a fixed polynomial for natural classes of graphs H with unbounded maximum degree, such as planar graphs and, more broadly, graphs with bounded degeneracy. More strikingly, we show that for almost every graph H, the degree of the polynomial that bounds the size of our combinatorial kernel grows only logarithmically in Δ(H). Our second kernel leverages linear-algebraic tools and involves the notion of faithful independent representations of graphs. It strengthens the general bound from prior work and, among other applications, yields near-optimal kernels for problems concerning the dimension of orthogonal graph representations over finite fields. We complement our kernelization results with conditional lower bounds, thereby nearly settling the kernel complexity of the problem for various target graphs H.
Cite as
Yael Berkman and Ishay Haviv. Kernelization for H-Coloring. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{berkman_et_al:LIPIcs.IPEC.2025.5,
author = {Berkman, Yael and Haviv, Ishay},
title = {{Kernelization for H-Coloring}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {5:1--5:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.5},
URN = {urn:nbn:de:0030-drops-251376},
doi = {10.4230/LIPIcs.IPEC.2025.5},
annote = {Keywords: Kernelization, Graph coloring, Graph homomorphism}
}
Document
Boundaried Kernelization via Representative Sets
Abstract
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or (conditionally) do not admit a kernelization where this size bound is polynomial, a so-called polynomial kernelization. Unfortunately, such polynomial kernelizations are known only in fairly restrictive settings where a small parameter value corresponds to a strong restriction on the global structure on the instance. Motivated by this, Antipov and Kratsch [WG 2025] proposed a local variant of kernelization, called boundaried kernelization, that requires only local structure to achieve a local improvement of the instance, which is in the spirit of protrusion replacement used in meta-kernelization [Bodlaender et al. JACM 2016]. They obtain polynomial boundaried kernelizations as well as (unconditional) lower bounds for several well-studied problems in kernelization.
In this work, we leverage the matroid-based techniques of Kratsch and Wahlström [JACM 2020] to obtain randomized polynomial boundaried kernelizations for s-Multiway Cut, Deletable Terminal Multiway Cut, Odd Cycle Transversal, and Vertex Cover[oct], for which randomized polynomial kernelizations in the usual sense were known before. A priori, these techniques rely on the global connectivity of the graph to identify reducible (irrelevant) vertices. Nevertheless, the separation of the local part by its boundary turns out to be sufficient for a local application of these methods.
Cite as
Leonid Antipov and Stefan Kratsch. Boundaried Kernelization via Representative Sets. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{antipov_et_al:LIPIcs.IPEC.2025.6,
author = {Antipov, Leonid and Kratsch, Stefan},
title = {{Boundaried Kernelization via Representative Sets}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {6:1--6:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.6},
URN = {urn:nbn:de:0030-drops-251386},
doi = {10.4230/LIPIcs.IPEC.2025.6},
annote = {Keywords: Parameterized complexity, boundaried kernelization, local preprocessing, representative sets method}
}
Document
Parameterized Complexity of Scheduling Unit-Time Jobs with Generalized Precedence Constraints
Abstract
We study the parameterized complexity of scheduling unit-time jobs on parallel, identical machines under generalized precedence constraints for minimization of the makespan and the sum of completion times (P|gen-prec, p_j = 1|γ, γ ∈ {C_max,∑_jC_j}). In our setting, each job is equipped with a Boolean formula (precedence constraint) over the set of jobs. A schedule satisfies a job’s precedence constraint if setting earlier jobs to true satisfies the formula. Our definition generalizes several common types of precedence constraints: classical and-constraints if every formula is a conjunction, or-constraints if every formula is a disjunction, and and/or-constraints if every formula is in conjunctive normal form. We prove fixed-parameter tractability when parameterizing by the number of predecessors. For parameterization by the number of successors, however, the complexity depends on the structure of the precedence constraints. If every constraint is a conjunction or a disjunction, we prove the problem to be fixed-parameter tractable. For constraints in disjunctive normal form, we prove W[1]-hardness. We show that the and/or-constrained problem is NP-hard, even for a single successor. Moreover, we prove NP-hardness on two machines if every constraint is a conjunction or a disjunction. This result not only proves para-NP-hardness for parameterization by the number of machines but also complements the polynomial-time solvability on two machines if every constraint is a conjunction [Coffman and Graham, 1972] or if every constraint is a disjunction [Johannes, 2005].
Cite as
Christina Büsing, Maurice Draeger, and Corinna Mathwieser. Parameterized Complexity of Scheduling Unit-Time Jobs with Generalized Precedence Constraints. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{busing_et_al:LIPIcs.IPEC.2025.7,
author = {B\"{u}sing, Christina and Draeger, Maurice and Mathwieser, Corinna},
title = {{Parameterized Complexity of Scheduling Unit-Time Jobs with Generalized Precedence Constraints}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {7:1--7:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.7},
URN = {urn:nbn:de:0030-drops-251390},
doi = {10.4230/LIPIcs.IPEC.2025.7},
annote = {Keywords: scheduling, precedence constraints, fixed-parameter tractability, complexity}
}
Document
Binary k-Center with Missing Entries: Structure Leads to Tractability
Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics.
Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as
Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
author = {Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
title = {{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {8:1--8:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
URN = {urn:nbn:de:0030-drops-251403},
doi = {10.4230/LIPIcs.IPEC.2025.8},
annote = {Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange
Abstract
We study the parameterized complexity of a recently introduced multi-agent variant of the Kidney Exchange problem. Given a directed graph G and integers d and k, the standard problem asks whether G contains a packing of vertex-disjoint cycles, each of length ≤ d, covering at least k vertices in total. In the multi-agent setting we consider, the vertex set is partitioned over several agents who reject a cycle packing as solution if it can be modified into an alternative packing that covers more of their own vertices. A cycle packing is called rejection-proof if no agent rejects it and the problem asks whether such a packing exists that covers at least k vertices.
We exploit the sunflower lemma on a set packing formulation of the problem to give a kernel for this Σ₂^P-complete problem that is polynomial in k for all constant values of d. We also provide a 2^𝒪(k log k) + n^𝒪(1) algorithm based on it and show that this FPT algorithm is asymptotically optimal under the ETH. Further, we generalize the problem by including an additional positive integer c in the input that naturally captures how much agents can modify a given cycle packing to reject it. For every constant c, the resulting problem simplifies from being Σ₂^P-complete to NP-complete. The super-exponential lower bound already holds for c = 2, though. We present an ad-hoc single-exponential algorithm for c = 1. These results reveal an interesting discrepancy between the classical and parameterized complexity of the problem and give a good view of what makes it hard.
Cite as
Bart M. P. Jansen, Jeroen S. K. Lamme, and Ruben F. A. Verhaegh. An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.9,
author = {Jansen, Bart M. P. and Lamme, Jeroen S. K. and Verhaegh, Ruben F. A.},
title = {{An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {9:1--9:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.9},
URN = {urn:nbn:de:0030-drops-251414},
doi = {10.4230/LIPIcs.IPEC.2025.9},
annote = {Keywords: Parameterized complexity, Multi-agent kidney exchange, Kernelization, Set packing}
}
Document
Parameterized Complexity of Vehicle Routing
Abstract
The Vehicle Routing Problem (VRP) is a popular generalization of the Traveling Salesperson Problem. Instead of one salesperson traversing the entire weighted, undirected graph G, there are k vehicles available to jointly cover the set of clients C ⊆ V(G). Every vehicle must start at one of the depot vertices D ⊆ V(G) and return to its start. Capacitated Vehicle Routing (CVRP) additionally restricts the route of each vehicle by limiting the number of clients it can cover, the distance it can travel, or both.
In this work, we study the complexity of VRP and the three variants of CVRP for several parameterizations, in particular focusing on the treewidth of G. We present an FPT algorithm for VRP parameterized by treewidth. For CVRP, we prove paraNP- and W[⋅]-hardness for various parameterizations, including treewidth, thereby rendering the existence of FPT algorithms unlikely. In turn, we provide an XP algorithm for CVRP when parameterized by both treewidth and the vehicle capacity.
Cite as
Michelle Döring, Jan Fehse, Tobias Friedrich, Paula Marten, Niklas Mohrin, Kirill Simonov, Farehe Soheil, Jakob Timm, and Shaily Verma. Parameterized Complexity of Vehicle Routing. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{doring_et_al:LIPIcs.IPEC.2025.10,
author = {D\"{o}ring, Michelle and Fehse, Jan and Friedrich, Tobias and Marten, Paula and Mohrin, Niklas and Simonov, Kirill and Soheil, Farehe and Timm, Jakob and Verma, Shaily},
title = {{Parameterized Complexity of Vehicle Routing}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {10:1--10:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.10},
URN = {urn:nbn:de:0030-drops-251424},
doi = {10.4230/LIPIcs.IPEC.2025.10},
annote = {Keywords: Vehicle Routing Problem, Treewidth, Parameterized Complexity}
}
Document
Parameterized Algorithms for Diversity of Networks with Ecological Dependencies
Abstract
For a phylogenetic tree, the phylogenetic diversity of a set A of taxa is the total weight of edges on paths to A. Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be invested most efficiently. In recent years, efficient algorithms have been developed to find sets of taxa that maximize phylogenetic diversity either in a phylogenetic network or in a phylogenetic tree subject to ecological constraints, such as a food web. However, these aspects have mostly been studied independently. Since both factors are biologically important, it seems natural to consider them together.
In this paper, we introduce decision problems where, given a phylogenetic network, a food web, and integers k, and D, the task is to find a set of k taxa with phylogenetic diversity of at least D under the maximize all paths measure, while also satisfying viability conditions within the food web. Here, we consider different definitions of viability, which all demand that a "sufficient" number of prey species survive to support surviving predators.
We investigate the parameterized complexity of these problems and present several fixed-parameter tractable (FPT) algorithms. Specifically, we provide a complete complexity dichotomy characterizing which combinations of parameters - out of the size constraint k, the acceptable diversity loss D̄, the scanwidth of the food web sw_ℱ, the maximum in-degree δ in the network, and the network height h - lead to W[1]-hardness and which admit FPT algorithms.
Our primary methodological contribution is a novel algorithmic framework for solving phylogenetic diversity problems in networks where dependencies (such as those from a food web) impose an order, using a color coding approach.
Cite as
Mark Jones and Jannik Schestag. Parameterized Algorithms for Diversity of Networks with Ecological Dependencies. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{jones_et_al:LIPIcs.IPEC.2025.11,
author = {Jones, Mark and Schestag, Jannik},
title = {{Parameterized Algorithms for Diversity of Networks with Ecological Dependencies}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {11:1--11:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.11},
URN = {urn:nbn:de:0030-drops-251439},
doi = {10.4230/LIPIcs.IPEC.2025.11},
annote = {Keywords: Phylogenetic Diversity, Fixed-Parameter Tractability, Phylogenetic Networks, Food Webs, Color Coding}
}
Document
Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set
Abstract
A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is Timeline Vertex Cover (also known as MinTimeline_∞), a temporal analogue to the classical Vertex Cover problem. In this problem, one is given a temporal graph 𝒢 and two integers k and 𝓁, and the goal is to cover each edge of each snapshot by selecting for each vertex at most k activity intervals of length at most 𝓁 each. Here, an edge uv in the ith snapshot is covered, if an activity interval of u or v is active at time i. In this work, we continue the algorithmic study of Timeline Vertex Cover and introduce the Timeline Dominating Set problem where we want to dominate all vertices in each snapshot by the selected activity intervals.
We analyze both problems from a classical and parameterized point of view and also consider partial problem versions, where the goal is to cover (dominate) at least t edges (vertices) of the snapshots. With respect to the parameterized complexity, we consider the temporal graph parameters vertex-interval-membership-width (vimw) and interval-membership-width (imw). We show that all considered problems admit FPT-algorithms when parameterized by vimw+k+𝓁. This provides a smaller parameter combination than the ones used for previously known FPT-algorithms for Timeline Vertex Cover. Surprisingly, for imw+k+𝓁, Timeline Dominating Set turns out to be easier than Timeline Vertex Cover, by also admitting an FPT-algorithm, whereas the vertex cover version is NP-hard even if imw+k+𝓁 is constant. We also consider parameterization by combinations of n, the vertex set size, with k or 𝓁 and parameterization by t. Here, we show for example that both partial problems are fixed-parameter tractable for t which significantly improves and generalizes a previous result for a special case of Partial Timeline Vertex Cover with k = 1.
Cite as
Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{herrmann_et_al:LIPIcs.IPEC.2025.12,
author = {Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
title = {{Timeline Problems in Temporal Graphs: Vertex Cover vs. Dominating Set}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {12:1--12:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.12},
URN = {urn:nbn:de:0030-drops-251446},
doi = {10.4230/LIPIcs.IPEC.2025.12},
annote = {Keywords: NP-hard problem, FPT-algorithm, interval-membership-width, Color coding}
}
Document
On Maximum 2-Clubs
Abstract
We consider the Maximum 2-Club problem where one is given as input an undirected graph G = (V,E) and seeks a subset of vertices S of maximum size such that any pair of vertices in S is connected by a path of length at most 2 in the graph induced by S. This problem is a natural relaxation of the famous Maximum Clique problem where any pair of vertices must be connected by an edge. Maximum 2-Club has been well-studied and is known to be NP-complete even on split graphs. It can be solved exactly in O^*(1.62ⁿ) time, where n denotes the number of vertices of the input graph, while being polynomial-time solvable on several graph classes. Parameterized algorithms for structural parameters have also been considered, leading in particular to an algorithm with a double-exponential dependence in the parameter treewidth. Such an algorithm is actually the best one known for the larger parameter vertex cover size up to a constant in the exponent. We provide new results in both directions. We first prove that the double-exponential dependence for parameter vertex cover size is unavoidable under the Exponential Time Hypothesis (ETH). This answers a question left open by Hartung, Komusiewicz, Nichterlein and Suchỳ [Hartung et al., 2015]. Our result also implies that the problem cannot be solved in time sub-exponential in n even for split graphs. We then provide an exact algorithm for the problem restricted to chordal graphs, running in O^*(1.1996ⁿ) time, by reducing Maximum 2-Club on this class to Maximum Independent Set on arbitrary graphs with the same number of vertices. The same reduction shows that we can enumerate all maximum (and inclusion-wise maximal) 2-clubs of a chordal graph in O^*(3^{n/3}) = O^*(1.4423ⁿ) time. We conclude by providing a construction of split graphs with Ω(3^{n/3}/poly(n)) maximum2-clubs, for some polynomial poly showing that the bound for enumeration is essentially tight.
Cite as
Joanne Dumont, Michael Lampis, Mathieu Liedloff, Anthony Perez, and Ioan Todinca. On Maximum 2-Clubs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dumont_et_al:LIPIcs.IPEC.2025.13,
author = {Dumont, Joanne and Lampis, Michael and Liedloff, Mathieu and Perez, Anthony and Todinca, Ioan},
title = {{On Maximum 2-Clubs}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.13},
URN = {urn:nbn:de:0030-drops-251454},
doi = {10.4230/LIPIcs.IPEC.2025.13},
annote = {Keywords: 2-clubs, chordal graphs, SETH, parameterized algorithms}
}
Document
A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma
Abstract
We present an algorithm for a class of n-fold ILPs whose existing algorithms in literature are often either (1) based on the augmentation framework where one starts with an arbitrary solution and then iteratively moves towards an optimal solution by solving appropriate programs; or (2) require solving a linear relaxation of the program; or (3) are based on decomposition/proximity based arguments. Combinatorial n-fold ILPs is a class of n-fold ILPs introduced and studied by Knop et al. [MP2020] that captures several other problems in a variety of domains. We present a simple and direct algorithm that solves combinatorial n-fold ILPs with unbounded non-negative variables via an application of the Steinitz lemma. Depending on the structure of the input ILP, we also improve upon the existing algorithms in the literature in terms of the running time, thereby showing an improvement that mirrors the one shown by Rohwedder [ICALP2025] contemporaneously and independently.
Cite as
Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, and Meirav Zehavi. A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gupta_et_al:LIPIcs.IPEC.2025.14,
author = {Gupta, Sushmita and Jain, Pallavi and Seetharaman, Sanjay and Zehavi, Meirav},
title = {{A Simple Algorithm for Combinatorial n-Fold ILPs Using the Steinitz Lemma}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {14:1--14:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.14},
URN = {urn:nbn:de:0030-drops-251467},
doi = {10.4230/LIPIcs.IPEC.2025.14},
annote = {Keywords: n-fold integer linear program, parameterized algorithms}
}
Document
New Algorithm for Combinatorial n-Folds and Applications
Abstract
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address n-fold ILPs where the matrix 𝒜 has a specific structure, i.e., where the blocks in the lower part of 𝒜 consist only of the row vectors (1,… ,1). In this paper, we propose an approach tailored to exactly these combinatorial n-folds. We utilize a divide and conquer approach to separate the original problem such that the right-hand side iteratively decreases in size. We show that this decrease in size can be calculated such that we only need to consider a bounded amount of possible right-hand sides. This, in turn, lets us efficiently combine solutions of the smaller right-hand sides to solve the original problem. We can decide the feasibility of, and also optimally solve, such problems in time (n r Δ)^O(r) log(‖b‖_∞), where n is the number of blocks, r the number of rows in the upper blocks and Δ = ‖A‖_∞.
We complement the algorithm by discussing applications of the n-fold ILPs with the specific structure we require. We consider the problems of (i) scheduling on uniform machines, (ii) closest string and (iii) (graph) imbalance. Regarding (i), our algorithm results in running times of p_max^O(d)|I|^O(1), matching a lower bound derived via ETH. For (ii) we achieve running times matching the current state-of-the-art in the general case. In contrast to the state-of-the-art, our result can leverage a bounded number of column-types to yield an improved running time. For (iii), we improve the parameter dependency on the size of the vertex cover.
Cite as
Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas. New Algorithm for Combinatorial n-Folds and Applications. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.15,
author = {Jansen, Klaus and Kahler, Kai and Pirotton, Lis and Tutas, Malte},
title = {{New Algorithm for Combinatorial n-Folds and Applications}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {15:1--15:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.15},
URN = {urn:nbn:de:0030-drops-251472},
doi = {10.4230/LIPIcs.IPEC.2025.15},
annote = {Keywords: integer linear programming, n-fold, parameterized complexity, scheduling, uniform machines}
}
Document
Designing Compact ILPs via Fast Witness Verification
Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints.
We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
Cite as
Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
author = {W{\l}odarczyk, Micha{\l}},
title = {{Designing Compact ILPs via Fast Witness Verification}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {16:1--16:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
URN = {urn:nbn:de:0030-drops-251481},
doi = {10.4230/LIPIcs.IPEC.2025.16},
annote = {Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
Treedepth Inapproximability and Exponential ETH Lower Bound
Abstract
Treedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a 2^{O(k²)} n-time exact algorithm and a polynomial-time O(OPT log^{3/2} OPT)-approximation algorithm, where the former algorithm returns an elimination forest of height k (witnessing that treedepth is at most k) for the n-vertex input graph G, or correctly reports that G has treedepth larger than k, and OPT is the actual value of the treedepth. On the complexity side, exactly computing treedepth is NP-complete, but the known reductions do not rule out a polynomial-time approximation scheme (PTAS), and under the Exponential Time Hypothesis (ETH) only exclude a running time of 2^o(√n) for exact algorithms.
We show that 1.0003-approximating Treedepth is NP-hard, and that exactly computing the treedepth of an n-vertex graph requires time 2^Ω(n), unless the ETH fails. We further derive that there exist absolute constants δ, c > 0 such that any (1+δ)-approximation algorithm requires time 2^Ω(n/log^c n). We do so via a simple direct reduction from Satisfiability to Treedepth, inspired by a reduction recently designed for Treewidth [STOC '25].
Cite as
Édouard Bonnet, Daniel Neuen, and Marek Sokołowski. Treedepth Inapproximability and Exponential ETH Lower Bound. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 17:1-17:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2025.17,
author = {Bonnet, \'{E}douard and Neuen, Daniel and Soko{\l}owski, Marek},
title = {{Treedepth Inapproximability and Exponential ETH Lower Bound}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {17:1--17:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.17},
URN = {urn:nbn:de:0030-drops-251494},
doi = {10.4230/LIPIcs.IPEC.2025.17},
annote = {Keywords: treedepth, lower bounds, approximation}
}
Document
Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth
Abstract
Many classical graph problems - such as Max Cut, Chromatic Number, Edge Dominating Set, and Hamiltonian Cycle - are polynomial-time solvable on cographs, fixed-parameter tractable (FPT) when parameterized by treewidth, but W[1]-hard when parameterized by clique-width. In contrast, Graph Isomorphism is FPT parameterized by treewidth, but for clique-width it is known to be in XP; whether it is FPT or W[1]-hard is open.
This reveals a sharp tractability gap between treewidth and clique-width. In this work, we propose a new structural graph parameter, 𝒞-modular-treewidth, which lies between treewidth and clique-width. The parameter leverages modular decomposition and restricts modules to induce graphs from a fixed class 𝒞 (e.g., cographs or edgeless graphs). By exploiting true and false twins - a hallmark of cograph-like structure - our parameter allows the design of efficient algorithms for several hard problems beyond the reach of treewidth-based methods. In this work, we show that 𝒞-modular-treewidth enables efficient solutions under suitable choices of 𝒞, opening a new pathway in the parameterized complexity landscape between treewidth and clique-width. In particular we show that
- When parameterized by cograph-modular-treewidth, Isomorphism admits an FPT algorithm, whereas Chromatic Number remains W[1]-hard.
- When parameterized by independent-modular-treewidth, Hamiltonian Cycle and Edge Dominating Set remain W[1]-hard.
Cite as
Václav Blažej, Satyabrata Jana, M. S. Ramanujan, and Peter Strulo. Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{blazej_et_al:LIPIcs.IPEC.2025.18,
author = {Bla\v{z}ej, V\'{a}clav and Jana, Satyabrata and Ramanujan, M. S. and Strulo, Peter},
title = {{Bridging Treewidth and Clique-Width via Cograph-Modular-Treewidth}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {18:1--18:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.18},
URN = {urn:nbn:de:0030-drops-251507},
doi = {10.4230/LIPIcs.IPEC.2025.18},
annote = {Keywords: Treewidth, Clique-width, Cograph, FPT, W\lbrack1\rbrack-hard}
}
Document
Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width
Abstract
Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].
Cite as
Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bojikian_et_al:LIPIcs.IPEC.2025.19,
author = {Bojikian, Narek and Kratsch, Stefan},
title = {{Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {19:1--19:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.19},
URN = {urn:nbn:de:0030-drops-251516},
doi = {10.4230/LIPIcs.IPEC.2025.19},
annote = {Keywords: Parameterized complexity, connected odd cycle transversal, clique-width}
}
Document
Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time
Abstract
In this paper, we give new and faster deterministic algorithms to count the number of k-paths and trees in host graphs of bounded treewidth. Our algorithms use time that is single-exponential in the treewidth, and employ the determinant method from [Hans L. Bodlaender et al., 2015]. Modifications of the algorithms count in single-exponential time the number of k-paths between specified end-points, the number of k-cycles, and the number of trees with k vertices that are a subgraph of the host graph.
Cite as
Jonne Visser and Hans L. Bodlaender. Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{visser_et_al:LIPIcs.IPEC.2025.20,
author = {Visser, Jonne and Bodlaender, Hans L.},
title = {{Deterministically Counting k-Paths and Trees Parameterized by Treewidth in Single-Exponential Time}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {20:1--20:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.20},
URN = {urn:nbn:de:0030-drops-251529},
doi = {10.4230/LIPIcs.IPEC.2025.20},
annote = {Keywords: Parameterized Complexity, Counting Subgraphs, #k-path, Dynamic Programming, Tree Decomposition, Determinant Method}
}
Document
A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs
Abstract
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithm due to Bouchitté and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vertices.
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Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden. A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{grigoriev_et_al:LIPIcs.IPEC.2025.21,
author = {Grigoriev, Alexander and Kobayashi, Yasuaki and Tamaki, Hisao and van der Zanden, Tom C.},
title = {{A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {21:1--21:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.21},
URN = {urn:nbn:de:0030-drops-251530},
doi = {10.4230/LIPIcs.IPEC.2025.21},
annote = {Keywords: potential maximal cliques, treewidth, planar graphs, triconnected planar graphs, polynomial delay generation}
}
Document
Efficient Enumeration of k-Plexes and k-Defective Cliques
Abstract
We investigate the enumeration of dense subgraphs under two well-known relaxations of cliques: k-plexes and k-defective cliques. Our main contribution is a family of algorithms with improved worst-case and output-sensitive complexities, driven by a decomposition technique based on graph degeneracy. We first propose a worst-case output-size near-optimal algorithm to enumerate all maximal k-plexes of size at least 2k-1, achieving a total time complexity of 𝒪(n(dk)³ 2^d Δ^k), where d is the degeneracy and Δ the maximum degree of the input graph. We then refine this result to obtain a fixed-parameter tractable output-sensitive algorithm with complexity 𝒪(α f(k) p(dΔ)), where α is the number of solutions, f(k) is an arbitrary function of k, and p is a polynomial. We then extend this framework to the enumeration of k-defective cliques and also show a linear-time O(n) algorithm for the enumeration of 2-plexes for graphs with bounded degeneracy. To the best of our knowledge, these complexities are competitive with or better than the current state of the art.
Cite as
Mohamed Jiddou and George Manoussakis. Efficient Enumeration of k-Plexes and k-Defective Cliques. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{jiddou_et_al:LIPIcs.IPEC.2025.22,
author = {Jiddou, Mohamed and Manoussakis, George},
title = {{Efficient Enumeration of k-Plexes and k-Defective Cliques}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {22:1--22:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.22},
URN = {urn:nbn:de:0030-drops-251545},
doi = {10.4230/LIPIcs.IPEC.2025.22},
annote = {Keywords: Parameterized complexity, enumeration algorithms, maximal cliques enumeration}
}
Document
Enumeration Kernels for Vertex Cover and Feedback Vertex Set
Abstract
Enumerative kernelization is a recent and promising area sitting at the intersection of parameterized complexity and enumeration algorithms. Its study began with the paper of Creignou et al. [Theory Comput. Syst., 2017], and development in the area has started to accelerate with the work of Golovach et al. [J. Comput. Syst. Sci., 2022]. The latter introduced polynomial-delay enumeration kernels and applied them in the study of structural parameterizations of the Matching Cut problem and some variants. Few other results, mostly on Longest Path and some generalizations of Matching Cut, have also been developed. However, little success has been seen in enumeration versions of Vertex Cover and Feedback Vertex Set, some of the most studied problems in kernelization. In this paper, we address this shortcoming. Our first result is a polynomial-delay enumeration kernel with 2k vertices for Enum Vertex Cover, where we wish to list all solutions with at most k vertices. This is obtained by developing a non-trivial lifting algorithm for the classical crown decomposition reduction rule, and directly improves upon the kernel with 𝒪(k²) vertices derived from the work of Creignou et al. Our other result is a polynomial-delay enumeration kernel with 𝒪(k³) vertices and edges for Enum Feedback Vertex Set; the proof is inspired by some ideas of Thomassé [TALG, 2010], but with a weaker bound on the kernel size due to difficulties in applying the q-expansion technique.
Cite as
Marin Bougeret, Guilherme C. M. Gomes, Vinicius F. dos Santos, and Ignasi Sau. Enumeration Kernels for Vertex Cover and Feedback Vertex Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bougeret_et_al:LIPIcs.IPEC.2025.23,
author = {Bougeret, Marin and C. M. Gomes, Guilherme and dos Santos, Vinicius F. and Sau, Ignasi},
title = {{Enumeration Kernels for Vertex Cover and Feedback Vertex Set}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {23:1--23:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.23},
URN = {urn:nbn:de:0030-drops-251552},
doi = {10.4230/LIPIcs.IPEC.2025.23},
annote = {Keywords: Kernelization, Enumeration, Vertex cover, Crown decomposition, Feedback vertex set}
}
Document
A Note on the Parameterised Complexity of Coverability in Vector Addition Systems
Abstract
We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): V ⊆ ℤ^d, an initial configuration s ∈ ℕ^d, and a target configuration t ∈ ℕ^d, decide whether starting from s, one can iteratively add vectors from V to ultimately arrive at a configuration that is larger than or equal to t on every coordinate, while not observing any negative value on any coordinate along the way. We consider two natural parameters for the problem: the dimension d and the size of V, defined as the total bitsize of its encoding. We present several results charting the complexity of those two parameterisations, among which the highlight is that coverability for VAS parameterised by the dimension and with all the numbers in the input encoded in unary is complete for the class XNL under PL-reductions. We also discuss open problems in the topic, most notably the question about fixed-parameter tractability for the parameterisation by the size of V.
Cite as
Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks. A Note on the Parameterised Complexity of Coverability in Vector Addition Systems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{pilipczuk_et_al:LIPIcs.IPEC.2025.24,
author = {Pilipczuk, Micha{\l} and Schmitz, Sylvain and Sinclair-Banks, Henry},
title = {{A Note on the Parameterised Complexity of Coverability in Vector Addition Systems}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {24:1--24:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.24},
URN = {urn:nbn:de:0030-drops-251563},
doi = {10.4230/LIPIcs.IPEC.2025.24},
annote = {Keywords: vector addition system, Petri net, parameterised complexity, coverability}
}
Document
Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas
Abstract
The Boolean connectivity problem asks whether the set of satisfying assignments of a given Boolean formula forms a connected subgraph in the n-dimensional hypercube. This problem is known to be coNP-complete, even when restricted to k-Horn formulas for k ≥ 3, as shown by Makino, Tamaki, and Yamamoto. In this paper, we further investigate the complexity of the Boolean connectivity problem for k-Horn formulas, referred to as Conn k-Horn. We first present an exact exponential-time algorithm for Conn k-Horn without any structural restrictions. Our algorithm builds on the deterministic PPZ algorithm proposed by Paturi, Pudlák, and Zane. It runs in O^*(2^{(1-1/2k)n}) time, achieving an exponential improvement over the previously known algorithm for the Boolean connectivity problem of k-CNF formulas, shown by Makino, Tamaki, and Yamamoto. We then examine both algorithmic and hardness results for Conn 3-Horn under bounded variable occurrences. On the algorithmic side, we propose a polynomial-time algorithm for Conn 3-Horn when each clause contains exactly three literals and each variable appears at most three times. This result generalizes to Conn k-Horn under the same structural constraints, in which each clause contains exactly k literals and each variable appears at most k times. On the hardness side, we prove that Conn 3-Horn remains coNP-complete even when restricted to instances in which each variable appears exactly four times.
Cite as
Takashi Horiyama, Yuto Okura, Kazuhisa Seto, and Junichi Teruyama. Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{horiyama_et_al:LIPIcs.IPEC.2025.25,
author = {Horiyama, Takashi and Okura, Yuto and Seto, Kazuhisa and Teruyama, Junichi},
title = {{Exact Algorithms and Hardness Result for the Boolean Connectivity Problem of k-Horn Formulas}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {25:1--25:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.25},
URN = {urn:nbn:de:0030-drops-251577},
doi = {10.4230/LIPIcs.IPEC.2025.25},
annote = {Keywords: k-Horn, Boolean connectivity, bounded variable occurrence, hardness, exact algorithm, satisfiability}
}
Document
Complexity of Local Search for CSPs Parameterized by Constraint Difference
Abstract
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset S of a universe U, the new input consists of a current solution P (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution S^*, the goal is to find a feasible solution as good as S^* in parameterized time f(k)⋅n^O(1), where k denotes the distance |PΔ S^*|. This model generalizes numerous classical parameterized optimization problems whose parameter k is the minimum number of elements removed from U to make it feasible, which corresponds to the case P = U.
We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where U is the set of constraints, and a subset U' of constraints is feasible if there is an assignment to the variables satisfying all constraints in U'. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate’s acceptance depends on the number of true literals.
Cite as
Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng. Complexity of Local Search for CSPs Parameterized by Constraint Difference. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{anand_et_al:LIPIcs.IPEC.2025.26,
author = {Anand, Aditya and Cohen-Addad, Vincent and D'Orsi, Tommaso and Gupta, Anupam and Lee, Euiwoong and Panigrahi, Debmalya and Peng, Sijin},
title = {{Complexity of Local Search for CSPs Parameterized by Constraint Difference}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {26:1--26:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.26},
URN = {urn:nbn:de:0030-drops-251586},
doi = {10.4230/LIPIcs.IPEC.2025.26},
annote = {Keywords: Constraint Satisfaction Problems, Parameterized Local Search, Optimization}
}
Document
Uniformity Within Parameterized Circuit Classes
Abstract
We study uniformity conditions for parameterized Boolean circuit families. Uniformity conditions require that the infinitely many circuits in a circuit family are in some sense easy to construct from one shared description. For shallow circuit families, logtime-uniformity is often desired but quite technical to prove. Despite that, proving it is often left as an exercise for the reader - even for recently introduced classes in parameterized circuit complexity, where uniformity conditions have not yet been explicitly studied. We formally define parameterized versions of linear-uniformity, logtime-uniformity, and FO-uniformity, and prove that these result in equivalent complexity classes when imposed on para-AC⁰ and para-AC^{0↑}. Overall, we provide a convenient way to verify uniformity for shallow parameterized circuit classes, and thereby substantiate claims of uniformity in the literature.
Cite as
Steef Hegeman, Jan Martens, and Alfons Laarman. Uniformity Within Parameterized Circuit Classes. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{hegeman_et_al:LIPIcs.IPEC.2025.27,
author = {Hegeman, Steef and Martens, Jan and Laarman, Alfons},
title = {{Uniformity Within Parameterized Circuit Classes}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {27:1--27:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.27},
URN = {urn:nbn:de:0030-drops-251598},
doi = {10.4230/LIPIcs.IPEC.2025.27},
annote = {Keywords: Parameterized complexity, circuit complexity, uniformity, descriptive complexity}
}
Document
Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number
Abstract
In the Geodetic Set problem, the input consists of a graph G and a positive integer k. The goal is to determine whether there exists a subset S of vertices of size k such that every vertex in the graph is included in a shortest path between two vertices in S. Kellerhals and Koana [IPEC 2020; J. Graph Algorithms Appl 2022] proved that the problem is W[1]-hard when parameterized by the pathwidth or the feedback vertex set number of the input graph. They posed the question of whether the problem admits an XP-algorithm when parameterized by the combination of these two parameters. We answer this in the negative by proving that the problem remains NP-hard even on graphs of constant pathwidth and feedback vertex set number.
Cite as
Prafullkumar Tale. Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{tale:LIPIcs.IPEC.2025.28,
author = {Tale, Prafullkumar},
title = {{Geodetic Set on Graphs of Constant Pathwidth and Feedback Vertex Set Number}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {28:1--28:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.28},
URN = {urn:nbn:de:0030-drops-251601},
doi = {10.4230/LIPIcs.IPEC.2025.28},
annote = {Keywords: Geodetic Sets, NP-hardness, Constant Treewidth}
}
Document
Hitting Geodesic Intervals in Structurally Restricted Graphs
Abstract
Given a graph G = (V,E), a set T of vertex pairs, and an integer k, Hitting Geodesic Intervals asks whether there is a set S ⊆ V of size at most k such that for each terminal pair {u,v} ∈ T, the set S intersects at least one shortest u-v path. Aravind and Saxena [WALCOM 2024] introduced this problem and showed several parameterized complexity results. In this paper, we extend the known results in both negative and positive directions and present sharp complexity contrasts with respect to structural graph parameters.
We first show that the problem is NP-complete even on graphs with highly restricted shortest-path structures. More precisely, we show the NP-completeness on graphs obtained by adding a single vertex to a disjoint union of 5-vertex paths. By modifying the proof of this result, we also show the NP-completeness on graphs obtained from a path by adding one vertex and on graphs obtained from a disjoint union of triangles by adding one universal vertex. Furthermore, we show the NP-completeness on graphs of bandwidth 4 and maximum degree 5 by replacing the universal vertex in the last case with a long path. Under standard complexity assumptions, these negative results rule out fixed-parameter algorithms for most of the structural parameters studied in the literature (if the solution size k is not part of the parameter).
We next present fixed-parameter algorithms parameterized by k plus modular-width and by k plus vertex integrity. The algorithm for the latter case does indeed solve a more general setting that includes the parameterization by the minimum vertex multiway-cut size of the terminal vertices. We show that this is tight in the sense that the problem parameterized by the minimum vertex multicut size of the terminal pairs is W[2]-complete. We then modify the proof of this intractability result and show that the problem is W[2]-complete parameterized by k even in the setting where T = binom(Q,2) for some Q ⊆ V.
Cite as
Tatsuya Gima, Yasuaki Kobayashi, Yuto Okada, Yota Otachi, and Hayato Takaike. Hitting Geodesic Intervals in Structurally Restricted Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{gima_et_al:LIPIcs.IPEC.2025.29,
author = {Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto and Otachi, Yota and Takaike, Hayato},
title = {{Hitting Geodesic Intervals in Structurally Restricted Graphs}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {29:1--29:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.29},
URN = {urn:nbn:de:0030-drops-251618},
doi = {10.4230/LIPIcs.IPEC.2025.29},
annote = {Keywords: Terminal monitoring set, Structural graph parameter, Geodesic interval}
}
Document
A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers
Abstract
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.
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Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler. A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{beisegel_et_al:LIPIcs.IPEC.2025.30,
author = {Beisegel, Jesse and Klost, Katharina and Knorr, Kristin and Ratajczak, Fabienne and Scheffler, Robert},
title = {{A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {30:1--30:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.30},
URN = {urn:nbn:de:0030-drops-251623},
doi = {10.4230/LIPIcs.IPEC.2025.30},
annote = {Keywords: Hamiltonian path, Hamiltonian cycle, partial order, graph width parameter, parameterized complexity}
}
Document
Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard
Abstract
We prove that Hamiltonian Path and Hamiltonian Cycle are NP-hard on graphs of linear mim-width 26, even when a linear order of the input graph with mim-width 26 is provided together with input. This fills a gap left by a broken proof of the para-NP-hardness of Hamiltonicity problems parameterized by mim-width.
Cite as
Benjamin Bergougnoux and Lars Jaffke. Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 31:1-31:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bergougnoux_et_al:LIPIcs.IPEC.2025.31,
author = {Bergougnoux, Benjamin and Jaffke, Lars},
title = {{Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {31:1--31:10},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.31},
URN = {urn:nbn:de:0030-drops-251631},
doi = {10.4230/LIPIcs.IPEC.2025.31},
annote = {Keywords: Hamiltonian Path, Hamiltonian Cycle, Mim-Width, Para-NP-Hardness}
}
Document
The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set
Abstract
The 10th iteration of the of the Parameterized Algorithms and Computational Experiments challenge (PACE) 2025 was devoted to engineer algorithms solving the Dominating Set problem as well as the Hitting Set problem. In contrast to the last iterations, these problems are (under standard assumptions) not fixed-parameter tractable (fpt) in general. However, restricting the structure of the input (e.g. to planar graphs or degenerate graphs for Dominating Set, or to set systems with sets of bounded size for Hitting Set) renders these problems fpt. Following the spirit of the last iterations of the PACE challenge, there is an exact track and a heuristic track for each problem; each track coming with a benchmark set of 100 public instances and 100 private instances. Overall, the PACE 2025 had 71 participants from 25 teams, 13 countries, and 3 continents. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.
Cite as
Mario Grobler and Sebastian Siebertz. The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{grobler_et_al:LIPIcs.IPEC.2025.32,
author = {Grobler, Mario and Siebertz, Sebastian},
title = {{The PACE 2025 Parameterized Algorithms and Computational Experiments Challenge: Dominating Set and Hitting Set}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {32:1--32:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.32},
URN = {urn:nbn:de:0030-drops-251644},
doi = {10.4230/LIPIcs.IPEC.2025.32},
annote = {Keywords: PACE 2025 Report, Dominating Set, Hitting Set, Algorithm Engineering, FPT, Heuristics}
}
Document
PACE Solver Description
PACE Solver Description: OBLX Exact Solver for the Dominating Set Problem
Abstract
We present and describe the solver OBLX for the Dominating Set problem on graphs. This solver was developed during the PACE challenge 2025 for the Exact track. It first applies several data reduction rules and performs a polynomial time reduction to Max Sat. The resulting Max Sat instance is in turn solved using the EvalMaxSat solver by Florent Avellaneda.
Cite as
Jona Dirks, Enna Gerhard, Victoria Kaial, and Lucas Lorieau. PACE Solver Description: OBLX Exact Solver for the Dominating Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 33:1-33:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dirks_et_al:LIPIcs.IPEC.2025.33,
author = {Dirks, Jona and Gerhard, Enna and Kaial, Victoria and Lorieau, Lucas},
title = {{PACE Solver Description: OBLX Exact Solver for the Dominating Set Problem}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {33:1--33:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.33},
URN = {urn:nbn:de:0030-drops-251659},
doi = {10.4230/LIPIcs.IPEC.2025.33},
annote = {Keywords: complexity theory, parameterized complexity, linear programming, java, dominating set, PACE 2025}
}
Document
PACE Solver Description
PACE Solver Description: Shadoks Approach to Minimum Hitting Set and Dominating Set
Abstract
Description of the solvers used by the Shadoks team in the PACE 2025 challenge. The challenge considers solvers for the minimum dominating set and hitting set problems. For the heuristic challenge, we respectively won third and fourth place for hitting set and dominating set. For the exact challenge, we won fifth place on both problems.
Cite as
Guilherme D. da Fonseca, Fabien Feschet, and Yan Gerard. PACE Solver Description: Shadoks Approach to Minimum Hitting Set and Dominating Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 34:1-34:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dafonseca_et_al:LIPIcs.IPEC.2025.34,
author = {da Fonseca, Guilherme D. and Feschet, Fabien and Gerard, Yan},
title = {{PACE Solver Description: Shadoks Approach to Minimum Hitting Set and Dominating Set}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {34:1--34:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.34},
URN = {urn:nbn:de:0030-drops-251660},
doi = {10.4230/LIPIcs.IPEC.2025.34},
annote = {Keywords: Optimization, heuristic, hitting set, dominating set}
}
Document
PACE Solver Description
PACE Solver Description: Bad Dominating Set Maker
Abstract
Dominating Set and Hitting Set are two well-known NP-hard problems on graphs and hypergraphs, respectively. For Dominating Set, we seek a subset S of vertices of minimum size, such that every vertex has a neighbor in S. For Hitting Set, we require that this minimum size subset S intersects each hyperedge. We present Bad Dominating Set Maker, our solver for both problems posed in the exact tracks of the 2025 PACE Challenge. It uses reduction rules, dynamic programming on tree decompositions, and external Vertex Cover and SAT solvers.
Cite as
Alexander Dobler, Simon Dominik Fink, and Mathis Rocton. PACE Solver Description: Bad Dominating Set Maker. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 35:1-35:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{dobler_et_al:LIPIcs.IPEC.2025.35,
author = {Dobler, Alexander and Fink, Simon Dominik and Rocton, Mathis},
title = {{PACE Solver Description: Bad Dominating Set Maker}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {35:1--35:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.35},
URN = {urn:nbn:de:0030-drops-251673},
doi = {10.4230/LIPIcs.IPEC.2025.35},
annote = {Keywords: Dominating Set, Hitting Set, Pace Challenge}
}
Document
PACE Solver Description
PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem
Abstract
In this paper, we describe the solver we submitted for both heuristic tracks of the PACE challenge 2025 on the dominating set problem and the hitting set problem. We solve both problems as unicost set covering problems. Our solver first performs reductions on the instance. Then greedy algorithms generate an initial solution that serves as starting point of the large neighborhood search and the local search which are executed afterwards. The solver ranked first in the dominating set heuristic track, and second in the hitting set heuristic track.
Cite as
Florian Fontan and Guillaume Verger. PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 36:1-36:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{fontan_et_al:LIPIcs.IPEC.2025.36,
author = {Fontan, Florian and Verger, Guillaume},
title = {{PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {36:1--36:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.36},
URN = {urn:nbn:de:0030-drops-251681},
doi = {10.4230/LIPIcs.IPEC.2025.36},
annote = {Keywords: dominating set, hitting set, unicost set covering, reductions, large neighborhood search, local search}
}
Document
PACE Solver Description
PACE Solver Description: Minimum Hitting Set Computation via Core-Guided MaxSAT Solving
Abstract
This paper describes our hybrid MaxSAT and mixed integer programming approach for finding minimum hitting sets as submitted to the 2025 PACE challenge. We also discuss hitting set specific challenges, lower bounds, preprocessing and design choices.
Cite as
André Schidler. PACE Solver Description: Minimum Hitting Set Computation via Core-Guided MaxSAT Solving. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 37:1-37:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{schidler:LIPIcs.IPEC.2025.37,
author = {Schidler, Andr\'{e}},
title = {{PACE Solver Description: Minimum Hitting Set Computation via Core-Guided MaxSAT Solving}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {37:1--37:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.37},
URN = {urn:nbn:de:0030-drops-251692},
doi = {10.4230/LIPIcs.IPEC.2025.37},
annote = {Keywords: hitting set, maxsat, core-guided}
}
Document
PACE Solver Description
PACE Solver Description: HitS&DoSeS - Exact and Heuristic Solvers for the Dominating Set and Hitting Set Problems
Abstract
This article briefly describes the most important algorithms and techniques used in HitS&DoSeS, a dominating set and hitting set solver submitted to the PACE 2025 contest (10th Parameterized Algorithms and Computational Experiments Challenge). Used approaches for the exact and heuristic tracks are described, for both the dominating set and the hitting set problems.
Cite as
Sylwester Swat. PACE Solver Description: HitS&DoSeS - Exact and Heuristic Solvers for the Dominating Set and Hitting Set Problems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 38:1-38:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{swat:LIPIcs.IPEC.2025.38,
author = {Swat, Sylwester},
title = {{PACE Solver Description: HitS\&DoSeS - Exact and Heuristic Solvers for the Dominating Set and Hitting Set Problems}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {38:1--38:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.38},
URN = {urn:nbn:de:0030-drops-251705},
doi = {10.4230/LIPIcs.IPEC.2025.38},
annote = {Keywords: dominating set, hitting set, exact algorithms, heuristic algorithms, large graphs, combinatorial optimization}
}
Document
PACE Solver Description
PACE Solver Description: UzL Solver for Dominating Set and Hitting Set
Abstract
This document contains a short description of our solver for the dominating set and hitting set problems that we submitted to the exact tracks of the PACE Challenge 2025. The solver is based on a straightforward MaxSAT formulation supplemented by hitting-set-based reduction rules. It utilizes a clique solver if the reduced instance is a (small) input for the vertex cover problem and tries to match certain lower bounds by expressing the reduced instance as a sat problem.
Cite as
Max Bannach, Florian Chudigiewitsch, and Marcel Wienöbst. PACE Solver Description: UzL Solver for Dominating Set and Hitting Set. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 39:1-39:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{bannach_et_al:LIPIcs.IPEC.2025.39,
author = {Bannach, Max and Chudigiewitsch, Florian and Wien\"{o}bst, Marcel},
title = {{PACE Solver Description: UzL Solver for Dominating Set and Hitting Set}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {39:1--39:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.39},
URN = {urn:nbn:de:0030-drops-251710},
doi = {10.4230/LIPIcs.IPEC.2025.39},
annote = {Keywords: exact algorithms, dominating set, hitting set}
}
Document
PACE Solver Description
PACE Solver Description: Weighting-Based Local Search Heuristic for the Hitting Set Problem
Abstract
We present a unified heuristic solver for the PACE 2025 challenge, addressing both the dominating set and hitting set problems by reducing them to the unicost set covering problem. Our solver applies standard reduction rules, a multi-round frequency-based greedy initializer, and a local search guided by adaptive element weights. Additional techniques, such as component-level exact solving and swap restriction, further enhance performance. In the final official evaluation, our proposed solver achieved second place in the heuristic track for the dominating set problem of the PACE 2025 challenge, while securing first place in the heuristic track for the hitting set problem.
Cite as
Canhui Luo, Qingyun Zhang, Zhouxing Su, and Zhipeng Lü. PACE Solver Description: Weighting-Based Local Search Heuristic for the Hitting Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 40:1-40:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
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@InProceedings{luo_et_al:LIPIcs.IPEC.2025.40,
author = {Luo, Canhui and Zhang, Qingyun and Su, Zhouxing and L\"{u}, Zhipeng},
title = {{PACE Solver Description: Weighting-Based Local Search Heuristic for the Hitting Set Problem}},
booktitle = {20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
pages = {40:1--40:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-407-9},
ISSN = {1868-8969},
year = {2025},
volume = {358},
editor = {Agrawal, Akanksha and van Leeuwen, Erik Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.40},
URN = {urn:nbn:de:0030-drops-251728},
doi = {10.4230/LIPIcs.IPEC.2025.40},
annote = {Keywords: PACE 2025, Dominating Set, Hitting Set, Heuristic Optimization, Weighted Local Search}
}