85 Search Results for "Lampis, Michael"

Document
DOI: 10.4230/LIPIcs.SAT.2026.18
D-QBF with Few Existential Variables Revisited

Authors: Andreas Grigorjew and Michael Lampis

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
Quantified Boolean Formula (QBF) is a notoriously hard generalization of SAT, especially from the point of view of parameterized complexity, where the problem remains intractable for most standard parameters. A recent work by Eriksson et al. [IJCAI 24] addressed this by considering the case where the propositional part of the formula is in CNF and we parameterize by the number k of existentially quantified variables. One of their main results was that this natural (but so far overlooked) parameter does lead to fixed-parameter tractability, if we also bound the maximum arity d of the clauses of the given CNF. Unfortunately, their algorithm has a double-exponential dependence on k (2^{2^k}), even when d is an absolute constant. Since the work of Eriksson et al. only complemented this with a SETH-based lower bound implying that a 2^{O(k)} dependence is impossible, this left a large gap as an open question. Our main result in this paper is to close this gap by showing that the double-exponential dependence is optimal, assuming the ETH: even for CNFs of arity 4, QBF with k existential variables cannot be solved in time 2^{2^o(k)} |φ|^O(1). Complementing this, we also consider the further restricted case of QBF with only two quantifier blocks (∀∃-QBF). We show that in this case the situation improves dramatically: for each d ≥ 3 we show an algorithm with running time k^O_d(k^{d-1}) |φ|^O(1) (where the notation O_d hides factors depending on d) and a lower bound under the ETH showing our algorithm is almost optimal.
Cite as

Andreas Grigorjew and Michael Lampis. D-QBF with Few Existential Variables Revisited. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grigorjew_et_al:LIPIcs.SAT.2026.18,
  author =	{Grigorjew, Andreas and Lampis, Michael},
  title =	{{D-QBF with Few Existential Variables Revisited}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.18},
  URN =		{urn:nbn:de:0030-drops-263244},
  doi =		{10.4230/LIPIcs.SAT.2026.18},
  annote =	{Keywords: QBF, FPT algorithms, ETH}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.85
Faster Algorithms for k-Orthogonal Vectors in Low Dimension

Authors: Anita Dürr, Evangelos Kipouridis, Michael Lampis, and Karol Węgrzycki

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
In the Orthogonal Vectors problem (OV), we are given two families A, B of subsets of {1,…,d}, each of size n, and the task is to decide whether there exists a pair a ∈ A and b ∈ B such that a ∩ b = ∅. Straightforward algorithms for this problem run in 𝒪(n² ⋅ d) or 𝒪(2^d ⋅ n) time, and assuming SETH, there is no 2^o(d)⋅ n^{2-ε} time algorithm that solves this problem for any constant ε > 0. Williams (FOCS 2024) presented a 𝒪̃(1.35^d ⋅ n)-time algorithm for the problem, based on the succinct equality-rank decomposition of the disjointness matrix. In this paper, we present a combinatorial algorithm that runs in randomized time 𝒪̃(1.25^d ⋅ n). This can be improved to 𝒪(1.16^d ⋅ n) using computer-aided evaluations. We also consider a more general k-Orthogonal Vectors problem, where given k families A_1,…,A_k of subsets of {1,…,d}, each of size n, the task is to find elements a_i ∈ A_i for every i ∈ {1,…,k} such that a₁ ∩ a₂ ∩ … ∩ a_k = ∅. We show that for every fixed k ⩾ 2, there exists ε_k > 0 such that the k-OV problem can be solved in time 𝒪(2^{(1 - ε_k)⋅d} ⋅ n). We also show that, asymptotically, this is the best we can hope for: for any ε > 0 there exists a k ⩾ 2 such that 2^{(1 - ε)⋅ d} ⋅ n^𝒪(1) time algorithm for k-Orthogonal Vectors would contradict the Set Cover Conjecture.
Cite as

Anita Dürr, Evangelos Kipouridis, Michael Lampis, and Karol Węgrzycki. Faster Algorithms for k-Orthogonal Vectors in Low Dimension. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 85:1-85:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{durr_et_al:LIPIcs.ICALP.2026.85,
  author =	{D\"{u}rr, Anita and Kipouridis, Evangelos and Lampis, Michael and W\k{e}grzycki, Karol},
  title =	{{Faster Algorithms for k-Orthogonal Vectors in Low Dimension}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{85:1--85:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.85},
  URN =		{urn:nbn:de:0030-drops-264747},
  doi =		{10.4230/LIPIcs.ICALP.2026.85},
  annote =	{Keywords: Orthogonal Vectors, Fine-grained Complexity, Exact Algorithms, Set Cover}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.25
Parameterized Critical Node Cut Revisited

Authors: Dušan Knop, Nikolaos Melissinos, and Manolis Vasilakis

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph G and integers k,x ≥ 0, Critical Node Cut (CNC) asks whether we can delete at most k vertices so that the number of remaining unordered pairs of connected vertices is at most x. CNC generalizes Vertex Cover (the case x = 0) and models tasks in network design, epidemiology, and social network analysis. We comprehensively map the structural parameterized complexity landscape for Critical Node Cut. First, we prove W[1]-hardness for the combined parameter k + fes + Δ + pw, where fes is the feedback edge set number, Δ the maximum degree, and pw the pathwidth of the input graph, respectively. This significantly improves over the known W[1]-hardness for k+tw, where tw denotes the treewidth, and is tight in that tree-depth together with maximum degree trivially yields FPT. Second, we give new positive results. Specifically, we identify three structural parameters-max-leaf number, vertex integrity, and modular-width-that render the problem fixed-parameter tractable, and develop a polynomial-time algorithm for graphs of constant clique-width. Third, leveraging a technique introduced by Lampis [ICALP '14], we develop an FPT approximation scheme that, for any ε > 0, computes a (1+ε)-approximate solution in time (tw / ε)^{𝒪(tw)} n^{𝒪(1)}. Finally, we show that CNC admits no polynomial kernel when parameterized by vertex cover number, unless standard assumptions fail. Together, these results substantially sharpen the known complexity landscape for CNC.
Cite as

Dušan Knop, Nikolaos Melissinos, and Manolis Vasilakis. Parameterized Critical Node Cut Revisited. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{knop_et_al:LIPIcs.SWAT.2026.25,
  author =	{Knop, Du\v{s}an and Melissinos, Nikolaos and Vasilakis, Manolis},
  title =	{{Parameterized Critical Node Cut Revisited}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.25},
  URN =		{urn:nbn:de:0030-drops-260617},
  doi =		{10.4230/LIPIcs.SWAT.2026.25},
  annote =	{Keywords: Critical Node Cut, Parameterized Complexity, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.28
The Parameterized Complexity of Coloring Mixed Graphs

Authors: Antonio Lauerbach, Konstanty Junosza-Szaniawski, Marie Diana Sieper, and Alexander Wolff

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring c of a mixed graph G assigns a positive integer to each vertex such that c(u)≠c(v) for every edge {u,v} and c(u)<c(v) for every arc (u,v) of G. As in classical coloring, the objective is to minimize the number of colors. Thus, mixed (graph) coloring generalizes classical coloring of undirected graphs and allows for more general applications, such as scheduling with precedence constraints, modeling metabolic pathways, and process management in operating systems; see a survey by Sotskov [Mathematics, 2020]. We initiate the systematic study of the parameterized complexity of mixed coloring. We focus on structural graph parameters that lie between cliquewidth and vertex cover, primarily with respect to the underlying undirected graph. Unlike classical coloring, which is fixed-parameter tractable (FPT) parameterized by treewidth or neighborhood diversity, we show that mixed coloring is W[1]-hard for treewidth and even paraNP-hard for neighborhood diversity. To utilize the directedness of arcs, we introduce and analyze natural generalizations of neighborhood diversity and cliquewidth to mixed graphs, and show that mixed coloring becomes FPT when parameterized by (the generalized) mixed neighborhood diversity. Further, we investigate how these parameters are affected if we add transitive arcs, which do not affect colorings. Finally, we provide tight bounds on the chromatic number of mixed graphs, generalizing known bounds on mixed interval graphs.
Cite as

Antonio Lauerbach, Konstanty Junosza-Szaniawski, Marie Diana Sieper, and Alexander Wolff. The Parameterized Complexity of Coloring Mixed Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lauerbach_et_al:LIPIcs.SWAT.2026.28,
  author =	{Lauerbach, Antonio and Junosza-Szaniawski, Konstanty and Sieper, Marie Diana and Wolff, Alexander},
  title =	{{The Parameterized Complexity of Coloring Mixed Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.28},
  URN =		{urn:nbn:de:0030-drops-260644},
  doi =		{10.4230/LIPIcs.SWAT.2026.28},
  annote =	{Keywords: Mixed Graphs, Coloring, Parameterized Complexity, Structural Graph Parameters}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.2
Man, These New York Times Games Are Hard! A Computational Perspective

Authors: Alessandro Giovanni Alberti, Flavio Chierichetti, Mirko Giacchini, Daniele Muscillo, Alessandro Panconesi, and Erasmo Tani

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper’s readership. In this paper, we bring the computational lens to the study of New York Times games and consider four of them not previously studied: Letter Boxed, Pips, Strands and Tiles. We show that these games can be just as hard as they are fun. In particular, we characterize the hardness of several variants of computational problems related to these popular puzzle games. For Letter Boxed, we show that deciding whether an instance is solvable is in general NP-Complete, while in some parameter settings it can be done in polynomial time. Similarly, for Pips we prove that deciding whether a puzzle has a solution is NP-Complete even in some restricted classes of instances. We then show that one natural computational problem arising from Strands is NP-Complete in most parameter settings. Finally, we demonstrate that deciding whether a Tiles puzzle is solvable with a single, uninterrupted combo requires polynomial time.
Cite as

Alessandro Giovanni Alberti, Flavio Chierichetti, Mirko Giacchini, Daniele Muscillo, Alessandro Panconesi, and Erasmo Tani. Man, These New York Times Games Are Hard! A Computational Perspective. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alberti_et_al:LIPIcs.FUN.2026.2,
  author =	{Alberti, Alessandro Giovanni and Chierichetti, Flavio and Giacchini, Mirko and Muscillo, Daniele and Panconesi, Alessandro and Tani, Erasmo},
  title =	{{Man, These New York Times Games Are Hard! A Computational Perspective}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.2},
  URN =		{urn:nbn:de:0030-drops-257219},
  doi =		{10.4230/LIPIcs.FUN.2026.2},
  annote =	{Keywords: NP-Hardness, Puzzles, Games, New York Times, Pips, Letter Boxed, Strands, Tiles}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.6
Ferry Cover with Connectivity Constraints

Authors: Niranjan Balachandran, Ankita Dargad, Urban Larsson, Neeldhara Misra, and Umesh Shankar

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
The classical Ferry Cover problem asks for the minimum boat capacity needed to transport all vertices of a graph across a river such that no edge remains on either bank at any time - a requirement that the banks induce stable (independent) sets. We study a natural generalization in which the banks must satisfy an arbitrary graph property. For hereditary properties such as acyclicity or planarity, we show that the structural characterization of small-boat and large-boat graphs established by Csorba, Hurkens, and Woeginger extends directly. We then turn to the connected-bank variant, where the property of interest - connectedness - is not hereditary: both banks must induce connected subgraphs throughout the transfer. We provide a complete characterization of graphs that can be transferred with a boat of size one (boat-1 graphs): a connected graph is boat-1 if and only if its block-cut tree is a path. This characterization yields a linear-time recognition algorithm. As a consequence, we show that every biconnected graph is boat-1, since such graphs admit an st-numbering. We also develop an efficient algorithm for determining the boat number of trees. Our work opens new directions for river-crossing problems under non-hereditary bank constraints.
Cite as

Niranjan Balachandran, Ankita Dargad, Urban Larsson, Neeldhara Misra, and Umesh Shankar. Ferry Cover with Connectivity Constraints. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{balachandran_et_al:LIPIcs.FUN.2026.6,
  author =	{Balachandran, Niranjan and Dargad, Ankita and Larsson, Urban and Misra, Neeldhara and Shankar, Umesh},
  title =	{{Ferry Cover with Connectivity Constraints}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.6},
  URN =		{urn:nbn:de:0030-drops-257253},
  doi =		{10.4230/LIPIcs.FUN.2026.6},
  annote =	{Keywords: ferry cover, river crossing, block-cut tree, st-numbering, hereditary graph property, connectivity}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.24
On the Complexity of the Maker-Breaker Happy Vertex Game

Authors: Mathieu Hilaire, Perig Montfort, and Nacim Oijid

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
Given a c-colored graph G, a vertex v of G is said to be happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li [Peng Zhang and Angsheng Li, 2015] to compute the homophily of a graph. Eto, Fujimoto, Kiya, Matsushita, Miyano, Murao and Saitoh [Hiroshi Eto et al., 2025] introduced the Maker-Maker version of the Happy vertex game, where two players compete to claim more happy vertices than their opponent. We introduce here the Maker-Breaker happy vertex game: two players, Maker and Breaker, alternately color the vertices of a graph with their respective colors. Maker aims to maximize the number of happy vertices at the end, while Breaker aims to prevent her. This game is also a scoring version of the Maker-Breaker domination game introduced by Duchene, Gledel, Parreau and Renault [Duchene et al., 2020], as a happy vertex corresponds exactly to a vertex that is not dominated in the domination game. Therefore, this game is a very natural game on graphs and can be studied within the scope of scoring positional games [Bagan et al., 2024]. We initiate here the complexity study of this game, by proving that computing its score is PSPACE-complete on trees, NP-hard on caterpillars, and polynomial on subdivided stars. Finally, we provide the exact value of the score on graphs of maximum degree 2, and we provide an FPT-algorithm to compute the score on graphs of bounded neighborhood diversity. An important contribution of the paper is that, to achieve our hardness results, we introduce a new type of incidence graph called the literal-clause incidence graph for 2-SAT formulas. We prove that QMAX 2-SAT remains PSPACE-complete even if this graph is acyclic, and that MAX 2-SAT remains NP-complete, even if this graph is acyclic and has maximum degree 2, i.e. is a union of paths. We demonstrate the importance of this contribution by proving that Incidence, the scoring positional game played on a graph is also PSPACE-complete when restricted to forests.
Cite as

Mathieu Hilaire, Perig Montfort, and Nacim Oijid. On the Complexity of the Maker-Breaker Happy Vertex Game. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hilaire_et_al:LIPIcs.FUN.2026.24,
  author =	{Hilaire, Mathieu and Montfort, Perig and Oijid, Nacim},
  title =	{{On the Complexity of the Maker-Breaker Happy Vertex Game}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{24:1--24:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.24},
  URN =		{urn:nbn:de:0030-drops-257434},
  doi =		{10.4230/LIPIcs.FUN.2026.24},
  annote =	{Keywords: Maker-Breaker game, Domination game, happy vertex game, scoring game, complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.
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Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.19
A Linear Kernel for Independent Set Reconfiguration in Planar Graphs

Authors: Nicolas Bousquet and Daniel W. Cranston

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Fix a positive integer r, and a graph G that is K_{3,r}-minor-free. Let I_s and I_t be two independent sets in G, each of size k. We begin with a "token" on each vertex of I_s and seek to move all tokens to I_t, by repeated "token jumping", removing a single token from one vertex and placing it on another vertex. We require that each intermediate arrangement of tokens again specifies an independent set of size k. Given G, I_s, and I_t, we ask whether there exists a sequence of token jumps that transforms I_s into I_t. When k is part of the input, this problem is known to be PSPACE-complete. But it was shown by Ito, Kamiński, and Ono [Ito et al., 2014] to be fixed-parameter tractable. That is, the problem can be solved in time f(k)⋅ P(n), for some function f and polynomial P, where n denotes the order of G. Here we strengthen the upper bound on the running time in terms of k by showing that the problem has a kernel of size linear in k. More precisely, we transform an arbitrary input problem on a K_{3,r}-minor-free graph (for some fixed positive integer r) into an equivalent problem on a (K_{3,r}-minor-free) graph with order O(k). This answers positively a question of Bousquet, Mouawad, Nishimura, and Siebertz [Nicolas Bousquet et al., 2022] and improves the recent quadratic kernel of Cranston, Mühlenthaler, and Peyrille [Daniel W. Cranston et al., 2024]. For planar graphs, we further strengthen this upper bound to get a kernel of size at most 42k.
Cite as

Nicolas Bousquet and Daniel W. Cranston. A Linear Kernel for Independent Set Reconfiguration in Planar Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bousquet_et_al:LIPIcs.STACS.2026.19,
  author =	{Bousquet, Nicolas and Cranston, Daniel W.},
  title =	{{A Linear Kernel for Independent Set Reconfiguration in Planar Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.19},
  URN =		{urn:nbn:de:0030-drops-255081},
  doi =		{10.4230/LIPIcs.STACS.2026.19},
  annote =	{Keywords: Reconfiguration, Independent Set, Kernel, Planar graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.53
Maximum Reachability Orientation of Mixed Graphs

Authors: Florian Hörsch

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph D, we use P(D) for the set of ordered pairs of distinct vertices in V(D) and we define κ_D:P(D) → {0,1} by κ_D(u,v) = 1 if v is reachable from u in D, and κ_D(u,v) = 0, otherwise. We use R(D) = ∑_{(u,v) ∈ P(D)}κ_D(u,v). Now, given a mixed graph G, we aim to find an orientation x⃑{G} of G that maximizes R(x⃑{G}). Hakimi, Schmeichel, and Young proved that the problem can be solved in polynomial time when restricted to undirected inputs. They inquired about the complexity in mixed graphs. We answer this question by showing that this problem is NP-hard, and, moreover, APX-hard. We then develop a finer understanding of how quickly the problem becomes difficult when going from undirected to mixed graphs. To this end, we consider the parameterized complexity of the problem with respect to the number k of preoriented arcs of G, a poorly studied form of parameterization. We show that the problem can be solved in time n^{O(k)} and that a (1-ε)-approximation can be computed in time f(k,ε)n^{O(1)} for any ε > 0.
Cite as

Florian Hörsch. Maximum Reachability Orientation of Mixed Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 53:1-53:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{horsch:LIPIcs.STACS.2026.53,
  author =	{H\"{o}rsch, Florian},
  title =	{{Maximum Reachability Orientation of Mixed Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{53:1--53:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.53},
  URN =		{urn:nbn:de:0030-drops-255421},
  doi =		{10.4230/LIPIcs.STACS.2026.53},
  annote =	{Keywords: orientations, mixed graphs, reachability, parameterized complexity, approximation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.30
A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers

Authors: Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

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.
Cite as

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
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

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
DOI: 10.4230/LIPIcs.IPEC.2025.3
Parameterized Maximum Node-Disjoint Paths

Authors: Michael Lampis and Manolis Vasilakis

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

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
DOI: 10.4230/LIPIcs.IPEC.2025.4
On the Complexity of Secluded Path Problems

Authors: Tesshu Hanaka and Daisuke Tsuru

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

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
DOI: 10.4230/LIPIcs.IPEC.2025.13
On Maximum 2-Clubs

Authors: Joanne Dumont, Michael Lampis, Mathieu Liedloff, Anthony Perez, and Ioan Todinca

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

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}
}
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