eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
1
644
10.4230/LIPIcs.IPEC.2023
article
LIPIcs, Volume 285, IPEC 2023, Complete Volume
Misra, Neeldhara
1
https://orcid.org/0000-0003-1727-5388
Wahlström, Magnus
2
https://orcid.org/0000-0002-0933-4504
IIT Gandhinagar, India
Royal Holloway, University of London, UK
LIPIcs, Volume 285, IPEC 2023, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023/LIPIcs.IPEC.2023.pdf
LIPIcs, Volume 285, IPEC 2023, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
0:i
0:xviii
10.4230/LIPIcs.IPEC.2023.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Misra, Neeldhara
1
https://orcid.org/0000-0003-1727-5388
Wahlström, Magnus
2
https://orcid.org/0000-0002-0933-4504
IIT Gandhinagar, India
Royal Holloway, University of London, UK
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.0/LIPIcs.IPEC.2023.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
1:1
1:18
10.4230/LIPIcs.IPEC.2023.1
article
Kernelizing Temporal Exploration Problems
Arrighi, Emmanuel
1
2
https://orcid.org/0000-0002-0326-1893
Fomin, Fedor V.
1
https://orcid.org/0000-0003-1955-4612
Golovach, Petr A.
1
https://orcid.org/0000-0002-2619-2990
Wolf, Petra
1
https://orcid.org/0000-0003-3097-3906
University of Bergen, Norway
University of Trier, Germany
We study the kernelization of exploration problems on temporal graphs. A temporal graph consists of a finite sequence of snapshot graphs 𝒢 = (G₁, G₂, … , G_L) that share a common vertex set but might have different edge sets. The non-strict temporal exploration problem (NS-TEXP for short) introduced by Erlebach and Spooner, asks if a single agent can visit all vertices of a given temporal graph where the edges traversed by the agent are present in non-strict monotonous time steps, i.e., the agent can move along the edges of a snapshot graph with infinite speed. The exploration must at the latest be completed in the last snapshot graph. The optimization variant of this problem is the k-arb NS-TEXP problem, where the agent’s task is to visit at least k vertices of the temporal graph. We show that under standard computational complexity assumptions, neither of the problems NS-TEXP nor k-arb NS-TEXP allow for polynomial kernels in the standard parameters: number of vertices n, lifetime L, number of vertices to visit k, and maximal number of connected components per time step γ; as well as in the combined parameters L+k, L + γ, and k+γ. On the way to establishing these lower bounds, we answer a couple of questions left open by Erlebach and Spooner.
We also initiate the study of structural kernelization by identifying a new parameter of a temporal graph p(𝒢) = ∑_{i=1}^L (|E(G_i)|) - |V(G)| + 1. Informally, this parameter measures how dynamic the temporal graph is. Our main algorithmic result is the construction of a polynomial (in p(𝒢)) kernel for the more general Weighted k-arb NS-TEXP problem, where weights are assigned to the vertices and the task is to find a temporal walk of weight at least k.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.1/LIPIcs.IPEC.2023.1.pdf
Temporal graph
temporal exploration
computational complexity
kernel
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
2:1
2:12
10.4230/LIPIcs.IPEC.2023.2
article
Cluster Editing with Overlapping Communities
Arrighi, Emmanuel
1
https://orcid.org/0000-0002-0326-1893
Bentert, Matthias
2
Drange, Pål Grønås
2
https://orcid.org/0000-0001-7228-6640
Sullivan, Blair D.
3
https://orcid.org/0000-0001-7720-6208
Wolf, Petra
2
https://orcid.org/0000-0003-3097-3906
University of Trier, Germany
University of Bergen, Norway
University of Utah, Salt Lake City, UT, USA
Cluster Editing, also known as correlation clustering, is a well-studied graph modification problem. In this problem, one is given a graph and allowed to perform up to k edge additions and deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. However, in real-world networks, clusters are often overlapping. For example, in social networks, a person might belong to several communities - e.g. those corresponding to work, school, or neighborhood. Another strong motivation comes from language networks where trying to cluster words with similar usage can be confounded by homonyms, that is, words with multiple meanings like "bat". The recently introduced operation of vertex splitting is one natural approach to incorporating such overlap into Cluster Editing. First used in the context of graph drawing, this operation allows a vertex v to be replaced by two vertices whose combined neighborhood is the neighborhood of v (and thus v can belong to more than one cluster). The problem of transforming a graph into a cluster graph using at most k edge additions, edge deletions, or vertex splits is called Cluster Editing with Vertex Splitting and is known to admit a polynomial kernel with respect to k and an O(9^{k²} + n + m)-time (parameterized) algorithm. However, it was not known whether the problem is NP-hard, a question which was originally asked by Abu-Khzam et al. [Combinatorial Optimization, 2018]. We answer this in the affirmative. We further give an improved algorithm running in O(2^{7klog k} + n + m) time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.2/LIPIcs.IPEC.2023.2.pdf
graph modification
correlation clustering
vertex splitting
NP-hardness
parameterized algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
3:1
3:15
10.4230/LIPIcs.IPEC.2023.3
article
Existential Second-Order Logic over Graphs: Parameterized Complexity
Bannach, Max
1
https://orcid.org/0000-0002-6475-5512
Chudigiewitsch, Florian
2
https://orcid.org/0000-0003-3237-1650
Tantau, Till
2
https://orcid.org/0000-0002-3946-8028
European Space Agency, Advanced Concepts Team, Noordwijk, The Netherlands
Universität zu Lübeck, Germany
By Fagin’s Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (eso formulas). Subsequent research refined this result, culminating in powerful theorems that characterize for each possible sequence of first-order quantifiers how difficult the described problem can be. We transfer this line of inquiry to the parameterized setting, where the size of the set quantified by the second-order quantifier is the parameter. Many natural parameterized problems can be described in this way using simple sequences of first-order quantifiers: For the clique or vertex cover problems, two universal first-order quantifiers suffice ("for all pairs of vertices ... must hold"); for the dominating set problem, a universal followed by an existential quantifier suffice ("for all vertices, there is a vertex such that ..."); and so on. We present a complete characterization that states for each possible sequence of first-order quantifiers how high the parameterized complexity of the described problems can be. The uncovered dividing line between quantifier sequences that lead to tractable versus intractable problems is distinct from that known from the classical setting, and it depends on whether the parameter is a lower bound on, an upper bound on, or equal to the size of the quantified set.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.3/LIPIcs.IPEC.2023.3.pdf
existential second-order logic
graph problems
parallel algorithms
fixed-parameter tractability
descriptive complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
4:1
4:12
10.4230/LIPIcs.IPEC.2023.4
article
On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model
Bentert, Matthias
1
Schestag, Jannik
2
3
https://orcid.org/0000-0001-7767-2970
Sommer, Frank
3
https://orcid.org/0000-0003-4034-525X
Department of Informatics, University of Bergen, Norway
Faculteit Elektrotechniek, Wiskunde en Informatica, TU Delft, The Netherlands
Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena, Germany
We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either safe or unsafe and we assume that failures only affect unsafe edges. In Unweighted Flexible Graph Connectivity we are given an undirected graph G = (V,E) in which the edge set E is partitioned into a set S of safe edges and a set U of unsafe edges and the task is to find a set T of at most k edges such that T - {u} is connected and spans V for any unsafe edge u ∈ T. Unweighted Flexible Graph Connectivity generalizes both Spanning Tree and Hamiltonian Cycle. We study Unweighted Flexible Graph Connectivity in terms of fixed-parameter tractability (FPT). We show an almost complete dichotomy on which parameters lead to fixed-parameter tractability and which lead to hardness. To this end, we obtain FPT-time algorithms with respect to the vertex deletion distance to cluster graphs and with respect to the treewidth. By exploiting the close relationship to Hamiltonian Cycle, we show that FPT-time algorithms for many smaller parameters are unlikely under standard parameterized complexity assumptions. Regarding problem-specific parameters, we observe that Unweighted Flexible Graph Connectivity admits an FPT-time algorithm when parameterized by the number of unsafe edges. Furthermore, we investigate a below-upper-bound parameter for the number of edges of a solution. We show that this parameter also leads to an FPT-time algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.4/LIPIcs.IPEC.2023.4.pdf
Flexible graph connectivity
NP-hard problem
parameterized complexity
below-guarantee parameterization
treewidth
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
5:1
5:14
10.4230/LIPIcs.IPEC.2023.5
article
Difference Determines the Degree: Structural Kernelizations of Component Order Connectivity
Bhyravarapu, Sriram
1
Jana, Satyabrata
1
https://orcid.org/0000-0002-7046-0091
Saurabh, Saket
1
2
https://orcid.org/0000-0001-7847-6402
Sharma, Roohani
3
https://orcid.org/0000-0003-2212-1359
The Institute of Mathematical Sciences, HBNI, Chennai, India
University of Bergen, Norway
Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
We consider the question of polynomial kernelization of a generalization of the classical Vertex Cover problem parameterized by a parameter that is provably smaller than the solution size. In particular, we focus on the c-Component Order Connectivity problem (c-COC) where given an undirected graph G and a non-negative integer t, the objective is to test whether there exists a set S of size at most t such that every component of G-S contains at most c vertices. Such a set S is called a c-coc set. It is known that c-COC admits a kernel with {O}(ct) vertices. Observe that for c = 1, this corresponds to the Vertex Cover problem.
We study the c-Component Order Connectivity problem parameterized by the size of a d-coc set (c-COC/d-COC), where c,d ∈ ℕ with c ≤ d. In particular, the input is an undirected graph G, a positive integer t and a set M of at most k vertices of G, such that the size of each connected component in G - M is at most d. The question is to find a set S of vertices of size at most t, such that the size of each connected component in G - S is at most c. In this paper, we give a kernel for c-COC/d-COC with O(k^{d-c+1}) vertices and O(k^{d-c+2}) edges. Our result exhibits that the difference in d and c, and not their absolute values, determines the exact degree of the polynomial in the kernel size.
When c = d = 1, the c-COC/d-COC problem is exactly the Vertex Cover problem parameterized by the solution size, which has a kernel with O(k) vertices and O(k²) edges, and this is asymptotically tight [Dell & Melkebeek, JACM 2014]. We also show that the dependence of d-c in the exponent of the kernel size cannot be avoided under reasonable complexity assumptions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.5/LIPIcs.IPEC.2023.5.pdf
Kernelization
Component Order Connectivity
Vertex Cover
Structural Parameterizations
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
6:1
6:19
10.4230/LIPIcs.IPEC.2023.6
article
The Parameterised Complexity Of Integer Multicommodity Flow
Bodlaender, Hans L.
1
https://orcid.org/0000-0002-9297-3330
Mannens, Isja
1
https://orcid.org/0000-0003-2295-0827
Oostveen, Jelle J.
1
https://orcid.org/0009-0009-4419-3143
Pandey, Sukanya
1
https://orcid.org/0000-0001-5728-1120
van Leeuwen, Erik Jan
1
https://orcid.org/0000-0001-5240-7257
Utrecht University, The Netherlands
The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Path problem, have been considered. Therefore, we investigate the parameterised complexity of the general Integer Multicommodity Flow problem. We show that the decision version of this problem on directed graphs for a constant number of commodities, when the capacities are given in unary, is XNLP-complete with pathwidth as parameter and XALP-complete with treewidth as parameter. When the capacities are given in binary, the problem is NP-complete even for graphs of pathwidth at most 13. We give related results for undirected graphs. These results imply that the problem is unlikely to be fixed-parameter tractable by these parameters.
In contrast, we show that the problem does become fixed-parameter tractable when weighted tree partition width (a variant of tree partition width for edge weighted graphs) is used as parameter.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.6/LIPIcs.IPEC.2023.6.pdf
multicommodity flow
parameterised complexity
XNLP-completeness
XALP-completeness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
7:1
7:13
10.4230/LIPIcs.IPEC.2023.7
article
Treewidth Is NP-Complete on Cubic Graphs
Bodlaender, Hans L.
1
https://orcid.org/0000-0002-9297-3330
Bonnet, Édouard
2
https://orcid.org/0000-0002-1653-5822
Jaffke, Lars
3
https://orcid.org/0000-0003-4856-5863
Knop, Dušan
4
https://orcid.org/0000-0003-2588-5709
Lima, Paloma T.
5
https://orcid.org/0000-0001-9304-4536
Milanič, Martin
6
https://orcid.org/0000-0002-8222-8097
Ordyniak, Sebastian
7
https://orcid.org/0000-0003-1935-651X
Pandey, Sukanya
1
https://orcid.org/0000-0001-5728-1120
Suchý, Ondřej
4
https://orcid.org/0000-0002-7236-8336
Utrecht University, The Netherlands
LIP, ENS Lyon, France
University of Bergen, Norway
Czech Technical University in Prague, Czech Republic
IT University of Copenhagen, Denmark
FAMNIT and IAM, University of Primorska, Koper, Slovenia
University of Leeds, UK
In this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9. We add a new and simpler proof of the NP-completeness of treewidth, and show that Treewidth remains NP-complete on subcubic induced subgraphs of the infinite 3-dimensional grid.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.7/LIPIcs.IPEC.2023.7.pdf
Treewidth
cubic graphs
degree
NP-completeness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
8:1
8:15
10.4230/LIPIcs.IPEC.2023.8
article
Stretch-Width
Bonnet, Édouard
1
https://orcid.org/0000-0002-1653-5822
Duron, Julien
1
https://orcid.org/0009-0004-0925-9438
Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
We introduce a new parameter, called stretch-width, that we show sits strictly between clique-width and twin-width. Unlike the reduced parameters [BKW '22], planar graphs and polynomial subdivisions do not have bounded stretch-width. This leaves open the possibility of efficient algorithms for a broad fragment of problems within Monadic Second-Order (MSO) logic on graphs of bounded stretch-width. In this direction, we prove that graphs of bounded maximum degree and bounded stretch-width have at most logarithmic treewidth. As a consequence, in classes of bounded stretch-width, Maximum Independent Set can be solved in subexponential time 2^{Õ(n^{8/9})} on n-vertex graphs, and, if further the maximum degree is bounded, Existential Counting Modal Logic [Pilipczuk '11] can be model-checked in polynomial time. We also give a polynomial-time O(OPT²)-approximation for the stretch-width of symmetric 0,1-matrices or ordered graphs.
Somewhat unexpectedly, we prove that exponential subdivisions of bounded-degree graphs have bounded stretch-width. This allows to complement the logarithmic upper bound of treewidth with a matching lower bound. We leave as open the existence of an efficient approximation algorithm for the stretch-width of unordered graphs, if the exponential subdivisions of all graphs have bounded stretch-width, and if graphs of bounded stretch-width have logarithmic clique-width (or rank-width).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.8/LIPIcs.IPEC.2023.8.pdf
Contraction sequences
twin-width
clique-width
algorithms
algorithmic metatheorems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
9:1
9:12
10.4230/LIPIcs.IPEC.2023.9
article
Minimum Separator Reconfiguration
C. M. Gomes, Guilherme
1
https://orcid.org/0000-0002-5164-1460
Legrand-Duchesne, Clément
2
https://orcid.org/0000-0002-4516-7336
Mahmoud, Reem
3
Mouawad, Amer E.
4
https://orcid.org/0000-0003-2481-4968
Okamoto, Yoshio
5
https://orcid.org/0000-0002-9826-7074
F. dos Santos, Vinicius
1
https://orcid.org/0000-0002-4608-4559
C. van der Zanden, Tom
6
https://orcid.org/0000-0003-3080-3210
Department of Computer Science, Federal, University of Minas Gerais, Belo Horizonte, Brazil
LaBRI, CNRS, Université de Bordeaux, France
Virginia Commonwealth University, Richmond, VA, USA
Department of Computer Science, American University of Beirut, Beirut, Lebanon
Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu, Japan
Department of Data Analytics and Digitalisation, Maastricht University, The Netherlands
We study the problem of reconfiguring one minimum s-t-separator A into another minimum s-t-separator B in some n-vertex graph G containing two non-adjacent vertices s and t. We consider several variants of the problem as we focus on both the token sliding and token jumping models. Our first contribution is a polynomial-time algorithm that computes (if one exists) a minimum-length sequence of slides transforming A into B. We additionally establish that the existence of a sequence of jumps (which need not be of minimum length) can be decided in polynomial time (by an algorithm that also outputs a witnessing sequence when one exists). In contrast, and somewhat surprisingly, we show that deciding if a sequence of at most 𝓁 jumps can transform A into B is an NP-complete problem. To complement this negative result, we investigate the parameterized complexity of what we believe to be the two most natural parameterized counterparts of the latter problem; in particular, we study the problem of computing a minimum-length sequence of jumps when parameterized by the size k of the minimum s-t-separators and when parameterized by the number 𝓁 of jumps. For the first parameterization, we show that the problem is fixed-parameter tractable, but does not admit a polynomial kernel unless NP ⊆ coNP/poly. We complete the picture by designing a kernel with 𝒪(𝓁²) vertices and edges for the length 𝓁 of the sequence as a parameter.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.9/LIPIcs.IPEC.2023.9.pdf
minimum separators
combinatorial reconfiguration
parameterized complexity
kernelization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
10:1
10:22
10.4230/LIPIcs.IPEC.2023.10
article
Kernels for the Disjoint Paths Problem on Subclasses of Chordal Graphs
Chaudhary, Juhi
1
https://orcid.org/0000-0001-5560-9129
Gahlawat, Harmender
1
https://orcid.org/0000-0001-7663-6265
Włodarczyk, Michal
2
https://orcid.org/0000-0003-0968-8414
Zehavi, Meirav
1
https://orcid.org/0000-0002-3636-5322
Ben-Gurion University of the Negev, Beersheba, Israel
University of Warsaw, Poland
Given an undirected graph G and a multiset of k terminal pairs 𝒳, the Vertex-Disjoint Paths (VDP) and Edge-Disjoint Paths (EDP) problems ask whether G has k pairwise internally vertex-disjoint paths and k pairwise edge-disjoint paths, respectively, connecting every terminal pair in 𝒳. In this paper, we study the kernelization complexity of VDP and EDP on subclasses of chordal graphs. For VDP, we design a 4k vertex kernel on split graphs and an 𝒪(k²) vertex kernel on well-partitioned chordal graphs. We also show that the problem becomes polynomial-time solvable on threshold graphs. For EDP, we first prove that the problem is NP-complete on complete graphs. Then, we design an 𝒪(k^{2.75}) vertex kernel for EDP on split graphs, and improve it to a 7k+1 vertex kernel on threshold graphs. Lastly, we provide an 𝒪(k²) vertex kernel for EDP on block graphs and a 2k+1 vertex kernel for clique paths. Our contributions improve upon several results in the literature, as well as resolve an open question by Heggernes et al. [Theory Comput. Syst., 2015].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.10/LIPIcs.IPEC.2023.10.pdf
Kernelization
Parameterized Complexity
Vertex-Disjoint Paths Problem
Edge-Disjoint Paths Problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
11:1
11:19
10.4230/LIPIcs.IPEC.2023.11
article
Parameterized Complexity Classification for Interval Constraints
Dabrowski, Konrad K.
1
https://orcid.org/0000-0001-9515-6945
Jonsson, Peter
2
https://orcid.org/0000-0002-5288-3330
Ordyniak, Sebastian
3
https://orcid.org/0000-0003-1935-651X
Osipov, George
2
https://orcid.org/0000-0002-2884-9837
Pilipczuk, Marcin
4
5
https://orcid.org/0000-0001-5680-7397
Sharma, Roohani
6
https://orcid.org/0000-0003-2212-1359
School of Computing, Newcastle University, UK
Department of Computer and Information Science, Linköping University, Sweden
School of Computing, University of Leeds, UK
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
IT University Copenhagen, Denmark
Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
Constraint satisfaction problems form a nicely behaved class of problems that lends itself to complexity classification results. From the point of view of parameterized complexity, a natural task is to classify the parameterized complexity of MinCSP problems parameterized by the number of unsatisfied constraints. In other words, we ask whether we can delete at most k constraints, where k is the parameter, to get a satisfiable instance. In this work, we take a step towards classifying the parameterized complexity for an important infinite-domain CSP: Allen’s interval algebra (IA). This CSP has closed intervals with rational endpoints as domain values and employs a set A of 13 basic comparison relations such as "precedes" or "during" for relating intervals. IA is a highly influential and well-studied formalism within AI and qualitative reasoning that has numerous applications in, for instance, planning, natural language processing and molecular biology. We provide an FPT vs. W[1]-hard dichotomy for MinCSP(Γ) for all Γ ⊆ A. IA is sometimes extended with unions of the relations in A or first-order definable relations over A, but extending our results to these cases would require first solving the parameterized complexity of Directed Symmetric Multicut, which is a notorious open problem. Already in this limited setting, we uncover connections to new variants of graph cut and separation problems. This includes hardness proofs for simultaneous cuts or feedback arc set problems in directed graphs, as well as new tractable cases with algorithms based on the recently introduced flow augmentation technique. Given the intractability of MinCSP(A) in general, we then consider (parameterized) approximation algorithms. We first show that MinCSP(A) cannot be polynomial-time approximated within any constant factor and continue by presenting a factor-2 fpt-approximation algorithm. Once again, this algorithm has its roots in flow augmentation.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.11/LIPIcs.IPEC.2023.11.pdf
(minimum) constraint satisfaction problem
Allen’s interval algebra
parameterized complexity
cut problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
12:1
12:16
10.4230/LIPIcs.IPEC.2023.12
article
An FPT Algorithm for Temporal Graph Untangling
Dondi, Riccardo
1
https://orcid.org/0000-0002-6124-2965
Lafond, Manuel
2
https://orcid.org/0000-0002-5305-7372
Università degli studi di Bergamo, Italy
Université de Sherbrooke, Canada
Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social networks. The problem asks to cover every temporal edge while minimizing the total span of the vertices (where the span of a vertex is the length of the timestamp interval it must remain active in). While the problem has been shown to be NP-hard even in very restricted cases, its parameterized complexity has not been fully understood. The problem is known to be in FPT under the span parameter only for graphs with two timestamps, but the parameterized complexity for the general case is open. We settle this open problem by giving an FPT algorithm that is based on a combination of iterative compression and a reduction to the Digraph Pair Cut problem, a powerful problem that has received significant attention recently.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.12/LIPIcs.IPEC.2023.12.pdf
Temporal Graphs
Vertex Cover
Graph Algorithms
Parameterized Complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
13:1
13:17
10.4230/LIPIcs.IPEC.2023.13
article
Budgeted Matroid Maximization: a Parameterized Viewpoint
Doron-Arad, Ilan
1
Kulik, Ariel
2
Shachnai, Hadas
1
Computer Science Department, Technion, Haifa, Israel
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an 𝓁-matchoid ℳ on a ground set E, a profit function p:E → ℝ_{≥ 0}, a cost function c:E → ℝ_{≥ 0}, and a budget B ∈ ℝ_{≥ 0}, the goal is to find in the 𝓁-matchoid a feasible set S of maximum profit p(S) subject to the budget constraint, i.e., c(S) ≤ B. The budgeted 𝓁-matchoid (BM) problem includes as special cases budgeted 𝓁-dimensional matching and budgeted 𝓁-matroid intersection. A strong motivation for studying BM from parameterized viewpoint comes from the APX-hardness of unbudgeted 𝓁-dimensional matching (i.e., B = ∞) already for 𝓁 = 3. Nevertheless, while there are known FPT algorithms for the unbudgeted variants of the above problems, the budgeted variants are studied here for the first time through the lens of parameterized complexity.
We show that BM parametrized by solution size is W[1]-hard, already with a degenerate single matroid constraint. Thus, an exact parameterized algorithm is unlikely to exist, motivating the study of FPT-approximation schemes (FPAS). Our main result is an FPAS for BM (implying an FPAS for 𝓁-dimensional matching and budgeted 𝓁-matroid intersection), relying on the notion of representative set - a small cardinality subset of elements which preserves the optimum up to a small factor. We also give a lower bound on the minimum possible size of a representative set which can be computed in polynomial time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.13/LIPIcs.IPEC.2023.13.pdf
budgeted matching
budgeted matroid intersection
knapsack problems
FPT-approximation scheme
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
14:1
14:21
10.4230/LIPIcs.IPEC.2023.14
article
Computing Complexity Measures of Degenerate Graphs
Drange, Pål Grønås
1
https://orcid.org/0000-0001-7228-6640
Greaves, Patrick
2
Muzi, Irene
2
https://orcid.org/0000-0003-2410-6523
Reidl, Felix
2
https://orcid.org/0000-0002-2354-3003
University of Bergen, Norway
Birkbeck, University of London, UK
We show that the VC-dimension of a graph can be computed in time n^{⌈log d+1⌉} d^{O(d)}, where d is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that see a specific subset of vertices inside of a (small) query set. The construction of this data structure takes time O(d2^dn), afterwards queries can be computed efficiently using fast Möbius inversion.
This data structure turns out to be useful for a range of tasks, especially for finding bipartite patterns in degenerate graphs, and we outline an efficient algorithm for counting the number of times specific patterns occur in a graph. The largest factor in the running time of this algorithm is O(n^c), where c is a parameter of the pattern we call its left covering number.
Concrete applications of this algorithm include counting the number of (non-induced) bicliques in linear time, the number of co-matchings in quadratic time, as well as a constant-factor approximation of the ladder index in linear time.
Finally, we supplement our theoretical results with several implementations and run experiments on more than 200 real-world datasets - the largest of which has 8 million edges - where we obtain interesting insights into the VC-dimension of real-world networks.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.14/LIPIcs.IPEC.2023.14.pdf
vc-dimension
datastructure
degeneracy
enumerating
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
15:1
15:17
10.4230/LIPIcs.IPEC.2023.15
article
An Improved Kernelization Algorithm for Trivially Perfect Editing
Dumas, Maël
1
Perez, Anthony
1
Univ. Orléans, INSA Centre Val de Loire, LIFO EA 4022, F-45067 Orléans, France
In the Trivially Perfect Editing problem one is given an undirected graph G = (V,E) and an integer k and seeks to add or delete at most k edges in G to obtain a trivially perfect graph. In a recent work, Dumas et al. [Dumas et al., 2023] proved that this problem admits a kernel with O(k³) vertices. This result heavily relies on the fact that the size of trivially perfect modules can be bounded by O(k²) as shown by Drange and Pilipczuk [Drange and Pilipczuk, 2018]. To obtain their cubic vertex-kernel, Dumas et al. [Dumas et al., 2023] then showed that a more intricate structure, so-called comb, can be reduced to O(k²) vertices. In this work we show that the bound can be improved to O(k) for both aforementioned structures and thus obtain a kernel with O(k²) vertices. Our approach relies on the straightforward yet powerful observation that any large enough structure contains unaffected vertices whose neighborhood remains unchanged by an editing of size k, implying strong structural properties.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.15/LIPIcs.IPEC.2023.15.pdf
Parameterized complexity
kernelization algorithms
graph modification
trivially perfect graphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
16:1
16:14
10.4230/LIPIcs.IPEC.2023.16
article
From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem
Eiben, Eduard
1
https://orcid.org/0000-0003-2628-3435
Ganian, Robert
2
https://orcid.org/0000-0002-7762-8045
Kanj, Iyad
3
https://orcid.org/0000-0003-1698-8829
Ordyniak, Sebastian
4
https://orcid.org/0000-0003-1935-651X
Szeider, Stefan
2
https://orcid.org/0000-0001-8994-1656
Department of Computer Science, Royal Holloway, University of London, Egham, UK
Algorithms and Complexity Group, TU Wien, Austria
School of Computing, DePaul University, Chicago, IL, USA
School of Computing, University of Leeds, UK
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formulated as classical graph problems on induced subgraphs of powers of partially-defined hypercubes.
In this paper, we follow up on this recent direction by investigating the Independent Set problem on this graph class, which has been studied in the data science setting under the name Diversity. We obtain a comprehensive picture of the problem’s parameterized complexity and establish its fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube.
Given that several such FO-definable problems have been shown to be fixed-parameter tractable on the considered graph class, one may ask whether fixed-parameter tractability could be extended to capture all FO-definable problems. We answer this question in the negative by showing that FO model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.16/LIPIcs.IPEC.2023.16.pdf
Independent Set
Powers of Hypercubes
Diversity
Parameterized Complexity
Incomplete Data
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
17:1
17:23
10.4230/LIPIcs.IPEC.2023.17
article
Approximate Monotone Local Search for Weighted Problems
Esmer, Barış Can
1
2
https://orcid.org/0000-0001-5694-1465
Kulik, Ariel
1
https://orcid.org/0000-0002-0533-3926
Marx, Dániel
1
https://orcid.org/0000-0002-5686-8314
Neuen, Daniel
3
https://orcid.org/0000-0002-4940-0318
Sharma, Roohani
4
https://orcid.org/0000-0003-2212-1359
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Saarbrücken Graduate School of Computer Science, Saarland Informatics Campus, Germany
University of Bremen, Germany
Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more generally, parameterized approximation algorithms. In this work, we generalize those results to the weighted setting.
More formally, we consider monotone subset minimization problems over a weighted universe of size n (e.g., Vertex Cover, d-Hitting Set and Feedback Vertex Set). We consider a model where the algorithm is only given access to a subroutine that finds a solution of weight at most α ⋅ W (and of arbitrary cardinality) in time c^k ⋅ n^{𝒪(1)} where W is the minimum weight of a solution of cardinality at most k. In the unweighted setting, Esmer et al. determine the smallest value d for which a β-approximation algorithm running in time dⁿ ⋅ n^{𝒪(1)} can be obtained in this model. We show that the same dependencies also hold in a weighted setting in this model: for every fixed ε > 0 we obtain a β-approximation algorithm running in time 𝒪((d+ε)ⁿ), for the same d as in the unweighted setting.
Similarly, we also extend a β-approximate brute-force search (in a model which only provides access to a membership oracle) to the weighted setting. Using existing approximation algorithms and exact parameterized algorithms for weighted problems, we obtain the first exponential-time β-approximation algorithms that are better than brute force for a variety of problems including Weighted Vertex Cover, Weighted d-Hitting Set, Weighted Feedback Vertex Set and Weighted Multicut.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.17/LIPIcs.IPEC.2023.17.pdf
parameterized approximations
exponential approximations
monotone local search
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
18:1
18:17
10.4230/LIPIcs.IPEC.2023.18
article
Consistency Checking Problems: A Gateway to Parameterized Sample Complexity
Ganian, Robert
1
https://orcid.org/0000-0002-7762-8045
Khazaliya, Liana
1
https://orcid.org/0009-0002-3012-7240
Simonov, Kirill
2
https://orcid.org/0000-0001-9436-7310
Technische Universität Wien, Austria
Hasso Plattner Institute, Universität Potsdam, Germany
Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a direct and provable correspondence between fixed-parameter PAC-learnability (in the sample complexity setting) and the fixed-parameter tractability of a corresponding "consistency checking" search problem (in the setting of computational complexity). The latter can be seen as generalizations of classical search problems where instead of receiving a single instance, one receives multiple yes- and no-examples and is tasked with finding a solution which is consistent with the provided examples.
Apart from a few initial results, consistency checking problems are almost entirely unexplored from a parameterized complexity perspective. In this article, we provide an overview of these problems and their connection to parameterized sample complexity, with the primary aim of facilitating further research in this direction. Afterwards, we establish the fixed-parameter (in)-tractability for some of the arguably most natural consistency checking problems on graphs, and show that their complexity-theoretic behavior is surprisingly very different from that of classical decision problems. Our new results cover consistency checking variants of problems as diverse as (k-)Path, Matching, 2-Coloring, Independent Set and Dominating Set, among others.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.18/LIPIcs.IPEC.2023.18.pdf
consistency checking
sample complexity
fixed-parameter tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
19:1
19:14
10.4230/LIPIcs.IPEC.2023.19
article
Finding Degree-Constrained Acyclic Orientations
Garvardt, Jaroslav
1
2
https://orcid.org/0000-0002-8762-8567
Renken, Malte
3
https://orcid.org/0000-0002-1450-1901
Schestag, Jannik
1
4
2
https://orcid.org/0000-0001-7767-2970
Weller, Mathias
3
https://orcid.org/0000-0002-9653-3690
Philipps-Universität Marburg, Germany
Friedrich-Schiller-Universität Jena, Germany
Technische Universität Berlin, Germany
Technische Universiteit Delft, The Netherlands
We consider the problem of orienting a given, undirected graph into a (directed) acyclic graph such that the in-degree of each vertex v is in a prescribed list λ(v). Variants of this problem have been studied for a long time and with various applications, but mostly without the requirement for acyclicity. Without this requirement, the problem is closely related to the classical General Factor problem, which is known to be NP-hard in general, but polynomial-time solvable if no list λ(v) contains large "gaps" [Cornuéjols, J. Comb. Theory B, 1988]. In contrast, we show that deciding if an acyclic orientation exists is NP-hard even in the absence of such "gaps".
On the positive side, we design parameterized algorithms for various, natural parameterizations of the acyclic orientation problem. A special case of the orientation problem with degree constraints recently came up in the context of reconstructing evolutionary histories (that is, phylogenetic networks). This phylogenetic setting imposes additional structure onto the problem that can be exploited algorithmically, allowing us to show fixed-parameter tractability when parameterized by either the treewidth of G (a smaller parameter than the frequently employed "level"), by the number of vertices v for which |λ(v)| ≥ 2, by the number of vertices v for which the highest value in λ(v) is at least 2. While the latter result can be extended to the general degree-constraint acyclic orientation problem, we show that the former cannot unless FPT=W[1].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.19/LIPIcs.IPEC.2023.19.pdf
Graph Orientation
Phylogenetic Networks
General Factor
NP-hardness
Parameterized Algorithms
Treewidth
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
20:1
20:19
10.4230/LIPIcs.IPEC.2023.20
article
Graph Clustering Problems Under the Lens of Parameterized Local Search
Garvardt, Jaroslav
1
https://orcid.org/0000-0002-8762-8567
Morawietz, Nils
1
https://orcid.org/0000-0002-7283-4982
Nichterlein, André
2
https://orcid.org/0000-0001-7451-9401
Weller, Mathias
2
https://orcid.org/0000-0002-9653-3690
Institute of Computer Science, Friedrich Schiller University Jena, Germany
Technische Universität Berlin, Germany
Cluster Editing is the problem of finding the minimum number of edge-modifications that transform a given graph G into a cluster graph G', that is, each connected component of G' is a clique. Similarly, in the Cluster Deletion problem, we further restrict the sought cluster graph G' to contain only edges that are also present in G. In this work, we consider the parameterized complexity of a local search variant for both problems: LS Cluster Deletion and LS Cluster Editing. Herein, the input also comprises an integer k and a partition 𝒞 of the vertex set of G that describes an initial cluster graph G^*, and we are to decide whether the "k-move-neighborhood" of G^* contains a cluster graph G' that is "better" (uses less modifications) than G^*. Roughly speaking, two cluster graphs G₁ and G₂ are k-move-neighbors if G₁ can be obtained from G₂ by moving at most k vertices to different connected components.
We consider parameterizations by k + 𝓁 for some natural parameters 𝓁, such as the number of clusters in 𝒞, the size of a largest cluster in 𝒞, or the cluster-vertex-deletion number (cvd) of G. Our main lower-bound results are that LS Cluster Editing is W[1]-hard when parameterized by k even if 𝒞 has size two and that both LS Cluster Deletion and LS Cluster Editing are W[1]-hard when parameterized by k + 𝓁, where 𝓁 is the size of the largest cluster of 𝒞. On the positive side, we show that both problems admit an algorithm that runs in k^{𝒪(k)}⋅ cvd^{3k} ⋅ n^{𝒪(1)} time and either finds a better cluster graph or correctly outputs that there is no better cluster graph in the k-move-neighborhood of the initial cluster graph.
As an intermediate result, we also obtain an algorithm that solves Cluster Deletion in cvd^{cvd} ⋅ n^{𝒪(1)} time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.20/LIPIcs.IPEC.2023.20.pdf
parameterized local search
permissive local search
FPT
W[1]-hardness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
21:1
21:15
10.4230/LIPIcs.IPEC.2023.21
article
Bandwidth Parameterized by Cluster Vertex Deletion Number
Gima, Tatsuya
1
https://orcid.org/0000-0003-2815-5699
Kim, Eun Jung
2
https://orcid.org/0000-0002-6824-0516
Köhler, Noleen
2
https://orcid.org/0000-0002-1023-6530
Melissinos, Nikolaos
3
https://orcid.org/0000-0002-0864-9803
Vasilakis, Manolis
2
https://orcid.org/0000-0001-6505-2977
JSPS Research Fellow, Nagoya University, Japan
Université Paris-Dauphine, PSL University, CNRS UMR7243, LAMSADE, Paris, France
Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Given a graph G and an integer b, Bandwidth asks whether there exists a bijection π from V(G) to {1, …, |V(G)|} such that max_{{u, v} ∈ E(G)} | π(u) - π(v) | ≤ b. This is a classical NP-complete problem, known to remain NP-complete even on very restricted classes of graphs, such as trees of maximum degree 3 and caterpillars of hair length 3. In the realm of parameterized complexity, these results imply that the problem remains NP-hard on graphs of bounded pathwidth, while it is additionally known to be W[1]-hard when parameterized by the treedepth of the input graph. In contrast, the problem does become FPT when parameterized by the vertex cover number of the input graph. In this paper, we make progress towards the parameterized (in)tractability of Bandwidth. We first show that it is FPT when parameterized by the cluster vertex deletion number cvd plus the clique number ω of the input graph, thus generalizing the previously mentioned result for vertex cover. On the other hand, we show that Bandwidth is W[1]-hard when parameterized only by cvd. Our results generalize some of the previous results and narrow some of the complexity gaps.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.21/LIPIcs.IPEC.2023.21.pdf
Bandwidth
Clique number
Cluster vertex deletion number
Parameterized complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
22:1
22:18
10.4230/LIPIcs.IPEC.2023.22
article
Collective Graph Exploration Parameterized by Vertex Cover
Gupta, Siddharth
1
https://orcid.org/0000-0003-4671-9822
Sa'ar, Guy
2
Zehavi, Meirav
2
https://orcid.org/0000-0002-3636-5322
BITS Pilani, Goa Campus, India
Ben Gurion University of the Negev, Beersheba, Israel
We initiate the study of the parameterized complexity of the Collective Graph Exploration (CGE) problem. In CGE, the input consists of an undirected connected graph G and a collection of k robots, initially placed at the same vertex r of G, and each one of them has an energy budget of B. The objective is to decide whether G can be explored by the k robots in B time steps, i.e., there exist k closed walks in G, one corresponding to each robot, such that every edge is covered by at least one walk, every walk starts and ends at the vertex r, and the maximum length of any walk is at most B. Unfortunately, this problem is NP-hard even on trees [Fraigniaud et al., 2006]. Further, we prove that the problem remains W[1]-hard parameterized by k even for trees of treedepth 3. Due to the para-NP-hardness of the problem parameterized by treedepth, and motivated by real-world scenarios, we study the parameterized complexity of the problem parameterized by the vertex cover number (vc) of the graph, and prove that the problem is fixed-parameter tractable (FPT) parameterized by vc. Additionally, we study the optimization version of CGE, where we want to optimize B, and design an approximation algorithm with an additive approximation factor of O(vc).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.22/LIPIcs.IPEC.2023.22.pdf
Collective Graph Exploration
Parameterized Complexity
Approximation Algorithm
Vertex Cover
Treedepth
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
23:1
23:22
10.4230/LIPIcs.IPEC.2023.23
article
Drawn Tree Decomposition: New Approach for Graph Drawing Problems
Gupta, Siddharth
1
https://orcid.org/0000-0003-4671-9822
Sa'ar, Guy
2
Zehavi, Meirav
2
https://orcid.org/0000-0002-3636-5322
BITS Pilani, Goa Campus, India
Ben Gurion University of the Negev, Beersheba, Israel
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such algorithms. An even more serious issue is that, here, "standard" parameters very often yield intractability. In particular, for the most common structural parameter, namely, treewidth, we frequently observe NP-hardness already when the input graphs are restricted to have constant (often, being just 1 or 2) treewidth.
Our work deals with both drawbacks simultaneously. We introduce a novel form of tree decomposition that, roughly speaking, does not decompose (only) a graph, but an entire drawing. As such, its bags and separators are of geometric (rather than only combinatorial) nature. While the corresponding parameter - like treewidth - can be arbitrarily smaller than the height (and width) of the drawing, we show that - unlike treewidth - it gives rise to efficient algorithms. Specifically, we get slice-wise polynomial (XP) time algorithms parameterized by our parameter. We present a general scheme for the design of such algorithms, and apply it to several central problems in Graph Drawing, including the recognition of grid graphs, minimization of crossings and bends, and compaction. Other than for the class of problems we discussed in the paper, we believe that our decomposition and scheme are of independent interest and can be further extended or generalized to suit even a wider class of problems. Additionally, we discuss classes of drawings where our parameter is bounded by 𝒪(√n) (where n is the number of vertices of the graph), yielding subexponential-time algorithms. Lastly, we prove which relations exist between drawn treewidth and other width measures, including treewidth, pathwidth, (dual) carving-width and embedded-width.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.23/LIPIcs.IPEC.2023.23.pdf
Graph Drawing
Parameterized Complexity
Tree decomposition
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
24:1
24:15
10.4230/LIPIcs.IPEC.2023.24
article
Single Machine Scheduling with Few Deadlines
Heeger, Klaus
1
https://orcid.org/0000-0001-8779-0890
Hermelin, Danny
1
https://orcid.org/0000-0002-6379-0383
Shabtay, Dvir
1
https://orcid.org/0000-0002-2709-599X
Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
We study single-machine scheduling problems with few deadlines. We focus on two classical objectives, namely minimizing the weighted number of tardy jobs and the total weighted completion time. For both problems, we give a pseudopolynomial-time algorithm for a constant number of different deadlines. This algorithm is complemented with an ETH-based, almost tight lower bound. Furthermore, we study the case where the number of jobs with a nontrivial deadline is taken as parameter. For this case, the complexity of our two problems differ: Minimizing the total number of tardy jobs becomes fixed-parameter tractable, while minimizing the total weighted completion time is W[1]-hard.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.24/LIPIcs.IPEC.2023.24.pdf
Single-machine scheduling
weighted completion time
tardy jobs
pseudopolynomial algorithms
parameterized complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
25:1
25:17
10.4230/LIPIcs.IPEC.2023.25
article
Twin-Width of Graphs with Tree-Structured Decompositions
Heinrich, Irene
1
https://orcid.org/0000-0001-9191-1712
Raßmann, Simon
1
https://orcid.org/0000-0003-1685-410X
Technische Universität Darmstadt, Germany
The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 [Édouard Bonnet et al., 2022; Édouard Bonnet et al., 2020], a mass of new results has appeared relating twin width to group theory, model theory, combinatorial optimization, and structural graph theory.
We take a detailed look at the interplay between the twin-width of a graph and the twin-width of its components under tree-structured decompositions: We prove that the twin-width of a graph is at most twice its strong tree-width, contrasting nicely with the result of [Édouard Bonnet and Hugues Déprés, 2023; Édouard Bonnet and Hugues Déprés, 2022], which states that twin-width can be exponential in tree-width. Further, we employ the fundamental concept from structural graph theory of decomposing a graph into highly connected components, in order to obtain optimal linear bounds on the twin-width of a graph given the widths of its biconnected components. For triconnected components we obtain a linear upper bound if we add red edges to the components indicating the splits which led to the components. Extending this approach to quasi-4-connectivity, we obtain a quadratic upper bound. Finally, we investigate how the adhesion of a tree decomposition influences the twin-width of the decomposed graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.25/LIPIcs.IPEC.2023.25.pdf
twin-width
quasi-4 connected components
strong tree-width
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
26:1
26:22
10.4230/LIPIcs.IPEC.2023.26
article
Dynamic Programming on Bipartite Tree Decompositions
Jaffke, Lars
1
Morelle, Laure
2
Sau, Ignasi
2
Thilikos, Dimitrios M.
2
Department of Informatics, University of Bergen, Norway
LIRMM, Université de Montpellier, CNRS, France
We revisit a graph width parameter that we dub bipartite treewidth, along with its associated graph decomposition that we call bipartite tree decomposition. Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number. Intuitively, a bipartite tree decomposition is a tree decomposition whose bags induce almost bipartite graphs and whose adhesions contain at most one vertex from the bipartite part of any other bag, while the width of such decomposition measures how far the bags are from being bipartite. Adapted from a tree decomposition originally defined by Demaine, Hajiaghayi, and Kawarabayashi [SODA 2010] and explicitly defined by Tazari [Theor. Comput. Sci. 2012], bipartite treewidth appears to play a crucial role for solving problems related to odd-minors, which have recently attracted considerable attention. As a first step toward a theory for solving these problems efficiently, the main goal of this paper is to develop dynamic programming techniques to solve problems on graphs of small bipartite treewidth. For such graphs, we provide a number of para-NP-completeness results, FPT-algorithms, and XP-algorithms, as well as several open problems. In particular, we show that K_t-Subgraph-Cover, Weighted Vertex Cover/Independent Set, Odd Cycle Transversal, and Maximum Weighted Cut are FPT parameterized by bipartite treewidth. We also provide the following complexity dichotomy when H is a 2-connected graph, for each of the H-Subgraph-Packing, H-Induced-Packing, H-Scattered-Packing, and H-Odd-Minor-Packing problems: if H is bipartite, then the problem is para-NP-complete parameterized by bipartite treewidth while, if H is non-bipartite, then the problem is solvable in XP-time. Beyond bipartite treewidth, we define 1-ℋ-treewidth by replacing the bipartite graph class by any graph class ℋ. Most of the technology developed here also works for this more general parameter.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.26/LIPIcs.IPEC.2023.26.pdf
tree decomposition
bipartite graphs
dynamic programming
odd-minors
packing
maximum cut
vertex cover
independent set
odd cycle transversal
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
27:1
27:15
10.4230/LIPIcs.IPEC.2023.27
article
Kernelization for Counting Problems on Graphs: Preserving the Number of Minimum Solutions
Jansen, Bart M. P.
1
https://orcid.org/0000-0001-8204-1268
van der Steenhoven, Bart
1
https://orcid.org/0009-0006-8816-5687
Eindhoven University of Technology, The Netherlands
A kernelization for a parameterized decision problem 𝒬 is a polynomial-time preprocessing algorithm that reduces any parameterized instance (x,k) into an instance (x',k') whose size is bounded by a function of k alone and which has the same yes/no answer for 𝒬. Such preprocessing algorithms cannot exist in the context of counting problems, when the answer to be preserved is the number of solutions, since this number can be arbitrarily large compared to k. However, we show that for counting minimum feedback vertex sets of size at most k, and for counting minimum dominating sets of size at most k in a planar graph, there is a polynomial-time algorithm that either outputs the answer or reduces to an instance (G',k') of size polynomial in k with the same number of minimum solutions. This shows that a meaningful theory of kernelization for counting problems is possible and opens the door for future developments. Our algorithms exploit that if the number of solutions exceeds 2^{poly(k)}, the size of the input is exponential in terms of k so that the running time of a parameterized counting algorithm can be bounded by poly(n). Otherwise, we can use gadgets that slightly increase k to represent choices among 2^{𝒪(k)} options by only poly(k) vertices.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.27/LIPIcs.IPEC.2023.27.pdf
kernelization
counting problems
feedback vertex set
dominating set
protrusion decomposition
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
28:1
28:18
10.4230/LIPIcs.IPEC.2023.28
article
On the Parameterized Complexity of Multiway Near-Separator
Jansen, Bart M. P.
1
https://orcid.org/0000-0001-8204-1268
Roy, Shivesh K.
1
https://orcid.org/0000-0003-0896-3437
Eindhoven University of Technology, The Netherlands
We study a new graph separation problem called Multiway Near-Separator. Given an undirected graph G, integer k, and terminal set T ⊆ V(G), it asks whether there is a vertex set S ⊆ V(G) ⧵ T of size at most k such that in graph G-S, no pair of distinct terminals can be connected by two pairwise internally vertex-disjoint paths. Hence each terminal pair can be separated in G-S by removing at most one vertex. The problem is therefore a generalization of (Node) Multiway Cut, which asks for a vertex set for which each terminal is in a different component of G-S. We develop a fixed-parameter tractable algorithm for Multiway Near-Separator running in time 2^{𝒪(k log k)} ⋅ n^{𝒪(1)}. Our algorithm is based on a new pushing lemma for solutions with respect to important separators, along with two problem-specific ingredients. The first is a polynomial-time subroutine to reduce the number of terminals in the instance to a polynomial in the solution size k plus the size of a given suboptimal solution. The second is a polynomial-time algorithm that, given a graph G and terminal set T ⊆ V(G) along with a single vertex x ∈ V(G) that forms a multiway near-separator, computes a 14-approximation for the problem of finding a multiway near-separator not containing x.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.28/LIPIcs.IPEC.2023.28.pdf
fixed-parameter tractability
multiway cut
near-separator
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
29:1
29:13
10.4230/LIPIcs.IPEC.2023.29
article
Sunflowers Meet Sparsity: A Linear-Vertex Kernel for Weighted Clique-Packing on Sparse Graphs
Jansen, Bart M. P.
1
https://orcid.org/0000-0001-8204-1268
Roy, Shivesh K.
1
https://orcid.org/0000-0003-0896-3437
Eindhoven University of Technology, The Netherlands
We study the kernelization complexity of the Weighted H-Packing problem on sparse graphs. For a fixed connected graph H, in the Weighted H-Packing problem the input is a graph G, a vertex-weight function w : V(G) → ℕ, and positive integers k, t. The question is whether there exist k vertex-disjoint subgraphs H₁, …, H_k of G such that H_i is isomorphic to H for each i ∈ [k] and the total weight of these k ⋅ |V(H)| vertices is at least t. It is known that the (unweighted) H-Packing problem admits a kernel with 𝒪(k^{|V(H)|-1}) vertices on general graphs, and a linear kernel on planar graphs and graphs of bounded genus. In this work, we focus on case that H is a clique on h ≥ 3 vertices (which captures Triangle Packing) and present a linear-vertex kernel for Weighted K_h-Packing on graphs of bounded expansion, along with a kernel with 𝒪(k^{1+ε}) vertices on nowhere-dense graphs for all ε > 0. To obtain these results, we combine two powerful ingredients in a novel way: the Erdős-Rado Sunflower lemma and the theory of sparsity.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.29/LIPIcs.IPEC.2023.29.pdf
kernelization
weighted problems
graph packing
sunflower lemma
bounded expansion
nowhere dense
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
30:1
30:12
10.4230/LIPIcs.IPEC.2023.30
article
How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks
Jones, Mark
1
https://orcid.org/0000-0002-4091-7089
Schestag, Jannik
1
2
https://orcid.org/0000-0001-7767-2970
TU Delft, The Netherlands
Friedrich-Schiller-Universität Jena, Germany
Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. We consider an extension of PD to phylogenetic networks. Given a phylogenetic network with weighted edges and a subset S of leaves, the all-paths phylogenetic diversity of S is the summed weight of all edges on a path from the root to some leaf in S. The problem of finding a bounded-size set S that maximizes this measure is polynomial-time solvable on trees, but NP-hard on networks. We study the latter from a parameterized perspective.
While this problem is W[2]-hard with respect to the size of S (and W[1]-hard with respect to the size of the complement of S), we show that it is FPT with respect to several other parameters, including the phylogenetic diversity of S, the acceptable loss of phylogenetic diversity, the number of reticulations in the network, and the treewidth of the underlying graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.30/LIPIcs.IPEC.2023.30.pdf
Phylogenetic Networks
Phylogenetic Diversity
Parameterized Complexity
W-hierarchy
FPT algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
31:1
31:17
10.4230/LIPIcs.IPEC.2023.31
article
Sidestepping Barriers for Dominating Set in Parameterized Complexity
Koutis, Ioannis
1
https://orcid.org/0000-0003-1535-3397
Włodarczyk, Michał
2
https://orcid.org/0000-0003-0968-8414
Zehavi, Meirav
3
https://orcid.org/0000-0002-3636-5322
New Jersey Institute of Technology, NJ, USA
University of Warsaw, Poland
Ben-Gurion University of the Negev, Beerhseba, Israel
We study the classic Dominating Set problem with respect to several prominent parameters. Specifically, we present algorithmic results that sidestep time complexity barriers by the incorporation of either approximation or larger parameterization. Our results span several parameterization regimes, including: (i,ii,iii) time/ratio-tradeoff for the parameters treewidth, vertex modulator to constant treewidth and solution size; (iv,v) FPT-algorithms for the parameters vertex cover number and feedback edge set number; and (vi) compression for the parameter feedback edge set number.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.31/LIPIcs.IPEC.2023.31.pdf
Dominating Set
Parameterized Complexity
Approximation Algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
32:1
32:17
10.4230/LIPIcs.IPEC.2023.32
article
Approximate Turing Kernelization and Lower Bounds for Domination Problems
Kratsch, Stefan
1
https://orcid.org/0000-0002-0193-7239
Kunz, Pascal
1
https://orcid.org/0000-0002-0787-8428
Algorithm Engineering, Humboldt-Universität zu Berlin, Germany
An α-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an (α c)-approximate solution for a parameterized optimization problem when given access to an oracle that can compute c-approximate solutions to instances with size bounded by a polynomial in the parameter. Hols et al. [ESA 2020] showed that a wide array of graph problems admit a (1+ε)-approximate polynomial Turing kernelization when parameterized by the treewidth of the graph and left open whether Dominating Set also admits such a kernelization.
We show that Dominating Set and several related problems parameterized by treewidth do not admit constant-factor approximate polynomial Turing kernelizations, even with respect to the much larger parameter vertex cover number, under certain reasonable complexity assumptions. On the positive side, we show that all of them do have a (1+ε)-approximate polynomial Turing kernelization for every ε > 0 for the joint parameterization by treewidth and maximum degree, a parameter which generalizes cutwidth, for example.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.32/LIPIcs.IPEC.2023.32.pdf
Approximate Turing kernelization
approximation lower bounds
exponential-time hypothesis
dominating set
capacitated dominating
connected dominating set
independent dominating set
treewidth
vertex cover number
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
33:1
33:20
10.4230/LIPIcs.IPEC.2023.33
article
A Parameterized Approximation Scheme for the Geometric Knapsack Problem with Wide Items
Mari, Mathieu
1
2
Picavet, Timothé
3
4
https://orcid.org/0000-0002-7129-0127
Pilipczuk, Michał
1
https://orcid.org/0000-0001-7891-1988
Institute of Informatics, University of Warsaw, Poland
IDEAS-NCBR, Warsaw, Poland
ENS de Lyon, France
Aalto University, Finland
We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box without overlap. Naturally, this problem is NP-complete. Recently, Grandoni et al. [ESA'19] showed that it is also 𝖶[1]-hard when parameterized by the size k of the sought packing, and they presented a parameterized approximation scheme (PAS) for the variant where we are allowed to rotate the rectangles by 90° before packing them into the box. Obtaining a PAS for the original 2D-Knapsack problem, without rotation, appears to be a challenging open question.
In this work, we make progress towards this goal by showing a PAS under the following assumptions:
- both the box and all the input rectangles have integral, polynomially bounded sidelengths;
- every input rectangle is wide - its width is greater than its height; and
- the aspect ratio of the box is bounded by a constant. Our approximation scheme relies on a mix of various parameterized and approximation techniques, including color coding, rounding, and searching for a structured near-optimum packing using dynamic programming.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.33/LIPIcs.IPEC.2023.33.pdf
Parameterized complexity
Approximation scheme
Geometric knapsack
Color coding
Dynamic programming
Computational geometry
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
34:1
34:15
10.4230/LIPIcs.IPEC.2023.34
article
A Contraction-Recursive Algorithm for Treewidth
Tamaki, Hisao
1
https://orcid.org/0000-0001-7566-8505
Meiji University, Kawasaki, Japan
Let tw(G) denote the treewidth of graph G. Given a graph G and a positive integer k such that tw(G) ≤ k + 1, we are to decide if tw(G) ≤ k. We give a certifying algorithm RTW ("R" for recursive) for this task: it returns one or more tree-decompositions of G of width ≤ k if the answer is YES and a minimal contraction H of G such that tw(H) > k otherwise. Starting from a greedy upper bound on tw(G) and repeatedly improving the upper bound by this algorithm, we obtain tw(G) with certificates.
RTW uses a heuristic variant of Tamaki’s PID algorithm for treewidth (ESA2017), which we call HPID. Informally speaking, PID builds potential subtrees of tree-decompositions of width ≤ k in a bottom up manner, until such a tree-decomposition is constructed or the set of potential subtrees is exhausted without success. HPID uses the same method of generating a new subtree from existing ones but with a different generation order which is not intended for exhaustion but for quick generation of a full tree-decomposition when possible. RTW, given G and k, interleaves the execution of HPID with recursive calls on G /e for edges e of G, where G / e denotes the graph obtained from G by contracting edge e. If we find that tw(G / e) > k, then we have tw(G) > k with the same certificate. If we find that tw(G / e) ≤ k, we "uncontract" the bags of the certifying tree-decompositions of G / e into bags of G and feed them to HPID to help progress. If the question is not resolved after the recursive calls are made for all edges, we finish HPID in an exhaustive mode. If it turns out that tw(G) > k, then G is a certificate for tw(G') > k for every G' of which G is a contraction, because we have found tw(G / e) ≤ k for every edge e of G. This final round of HPID guarantees the correctness of the algorithm, while its practical efficiency derives from our methods of "uncontracting" bags of tree-decompositions of G / e to useful bags of G, as well as of exploiting those bags in HPID.
Experiments show that our algorithm drastically extends the scope of practically solvable instances. In particular, when applied to the 100 instances in the PACE 2017 bonus set, the number of instances solved by our implementation on a typical laptop, with the timeout of 100, 1000, and 10000 seconds per instance, are 72, 92, and 98 respectively, while these numbers are 11, 38, and 68 for Tamaki’s PID solver and 65, 82, and 85 for his new solver (SEA 2022).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.34/LIPIcs.IPEC.2023.34.pdf
graph algorithm
treewidth
exact computation
BT dynamic programming
contraction
certifying algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
35:1
35:14
10.4230/LIPIcs.IPEC.2023.35
article
PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth
Bannach, Max
1
https://orcid.org/0000-0002-6475-5512
Berndt, Sebastian
2
https://orcid.org/0000-0003-4177-8081
European Space Agency, Advanced Concepts Team, Noordwijk, The Netherlands
Institute for Theoretical Computer Science, University of Lübeck, Germany
This article is a report by the challenge organizers on the 8th Parameterized Algorithms and Computational Experiments Challenge (PACE 2023). As was common in previous iterations of the competition, this year’s iteration implemented an exact and heuristic track for a parameterized problem that has gained attention in the theory community. This year, the problem was to compute the twinwidth of a graph, a recently introduced width parameter that measures the similarity of a graph to a cograph. In the exact track, the competition participants were asked to develop an exact algorithm that can solve as many instances as possible from a benchmark set of 100 instances - with a time limit of 30 minutes per instance. The same task must be accomplished within 5 minutes in the heuristic track. However, the result in this track is not required to be optimal.
As in previous iterations, the organizers handed out awards to the best solutions in both tracks and to the best student submissions. New this year is a dedicated theory award that appreciates new theoretical insights found by the participants during the development of their tools.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.35/LIPIcs.IPEC.2023.35.pdf
Twinwidth
Algorithm Engineering
FPT
Kernelization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
36:1
36:5
10.4230/LIPIcs.IPEC.2023.36
article
PACE Solver Description: Hydra Prime
Mizutani, Yosuke
1
https://orcid.org/0000-0002-9847-4890
Dursteler, David
1
https://orcid.org/0009-0000-6471-1504
Sullivan, Blair D.
1
https://orcid.org/0000-0001-7720-6208
University of Utah, Salt Lake City, UT, USA
This note describes our submission to the 2023 PACE Challenge on the computation of twin-width. Our solver Hydra Prime combines modular decomposition with a collection of upper- and lower-bound algorithms, which are alternatingly applied on the prime graphs resulting from the modular decomposition. We introduce two novel approaches which contributed to the solver’s winning performance in the Exact Track: timeline encoding and hydra decomposition. Timeline encoding is a new data structure for computing the width of a given contraction sequence, enabling faster local search; the hydra decomposition is an iterative refinement strategy featuring a small vertex separator.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.36/LIPIcs.IPEC.2023.36.pdf
Twin-width
PACE 2023
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
37:1
37:7
10.4230/LIPIcs.IPEC.2023.37
article
PACE Solver Description: Exact (GUTHMI) and Heuristic (GUTHM)
Leonhardt, Alexander
1
Dell, Holger
1
https://orcid.org/0000-0001-8955-0786
Haak, Anselm
1
Kammer, Frank
2
https://orcid.org/0000-0002-2662-3471
Meintrup, Johannes
2
https://orcid.org/0000-0003-4001-1153
Meyer, Ulrich
1
https://orcid.org/0000-0002-1197-3153
Penschuck, Manuel
1
https://orcid.org/0000-0003-2630-7548
Goethe University Frankfurt, Germany
THM, University of Applied Sciences , Mittelhessen, Gießen, Germany
Twin-width (tww) is a parameter measuring the similarity of an undirected graph to a co-graph [Édouard Bonnet et al., 2022]. It is useful to analyze the parameterized complexity of various graph problems. This paper presents two algorithms to compute the twin-width and to provide a contraction sequence as witness. The two algorithms are motivated by the PACE 2023 challenge, one for the exact track and one for the heuristic track. Each algorithm produces a contraction sequence witnessing (i) the minimal twin-width admissible by the graph in the exact track (ii) an upper bound on the twin-width as tight as possible in the heuristic track.
Our heuristic algorithm relies on several greedy approaches with different performance characteristics to find and improve solutions. For large graphs we use locality sensitive hashing to approximately identify suitable contraction candidates. The exact solver follows a branch-and-bound design. It relies on the heuristic algorithm to provide initial upper bounds, and uses lower bounds via contraction sequences to show the optimality of a heuristic solution found in some branch.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.37/LIPIcs.IPEC.2023.37.pdf
PACE 2023 Challenge
Heuristic
Exact
Twin-Width
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
38:1
38:4
10.4230/LIPIcs.IPEC.2023.38
article
PACE Solver Description: Touiouidth
Berthe, Gaétan
1
https://orcid.org/0000-0003-0017-6922
Coudert-Osmont, Yoann
2
Dobler, Alexander
3
https://orcid.org/0000-0002-0712-9726
Morelle, Laure
1
https://orcid.org/0009-0000-1001-1801
Reinald, Amadeus
1
https://orcid.org/0000-0002-8108-4036
Rocton, Mathis
3
https://orcid.org/0000-0002-7158-9022
LIRMM, CNRS, Université de Montpellier, France
Université de Lorraine, CNRS, Inria, LORIA, France
Algorithms and Complexity Group, TU Wien, Austria
We describe Touiouidth, a twin-width solver for the exact-track of the 2023 PACE Challenge: Twin Width. Our solver is based on a simple branch and bound algorithm with search space reductions and is implemented in C++.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.38/LIPIcs.IPEC.2023.38.pdf
Twinwidth
Pace Challenge
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
39:1
39:3
10.4230/LIPIcs.IPEC.2023.39
article
PACE Solver Description: Zygosity
Arrighi, Emmanuel
1
https://orcid.org/0000-0002-0326-1893
Drange, Pål Grønås
2
https://orcid.org/0000-0001-7228-6640
Langedal, Kenneth
2
https://orcid.org/0009-0001-6838-4640
Vadiee, Farhad
2
https://orcid.org/0000-0001-8106-2198
Vatshelle, Martin
2
Wolf, Petra
2
https://orcid.org/0000-0003-3097-3906
University of Trier, Germany
University of Bergen, Norway
The graph parameter twin-width was recently introduced by Bonnet et al. Twin-width is a parameter that measures a graph’s similarity to a cograph, which is a graph that can be reduced to a single vertex by repeatedly contracting twins. This brief description introduces Zygosity, a heuristic for computing a low-width contraction sequence that achieved second place in the 2023 edition of Parameterized Algorithms and Computational Experiments Challenge (PACE). Zygosity starts by repeatedly contracting twins. Then, any attached trees are contracted down to a single pendant vertex. The remaining graph is then contracted using a randomized greedy algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.39/LIPIcs.IPEC.2023.39.pdf
Twin-width
randomized greedy algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-12-13
285
40:1
40:5
10.4230/LIPIcs.IPEC.2023.40
article
PACE Solver Description: RedAlert - Heuristic Track
Bonnet, Édouard
1
https://orcid.org/0000-0002-1653-5822
Duron, Julien
1
https://orcid.org/0009-0004-0925-9438
Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
We present RedAlert, a heuristic solver for twin-width, submitted to the Heuristic Track of the 2023 edition of the Parameterized Algorithms and Computational Experiments (PACE) challenge.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol285-ipec2023/LIPIcs.IPEC.2023.40/LIPIcs.IPEC.2023.40.pdf
twin-width
contraction sequences
heuristic
pair sampling
pair filtering