183 Search Results for "Ganian, Robert"

Volume

LIPIcs, Volume 241

47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

MFCS 2022, August 22-26, 2022, Vienna, Austria

Editors: Stefan Szeider, Robert Ganian, and Alexandra Silva

Document
DOI: 10.4230/LIPIcs.SAT.2026.16
Bilateral Treewidth for QBF: Where Strategies and Resolution Meet

Authors: Robert Ganian and Marlene Gründel

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

Abstract
Treewidth is a well-studied decompositional parameter to measure the tree-likeness of a graph. While the propositional satisfiability problem (Sat) is known to be tractable when parameterized by the treewidth of the underlying primal graph, the evaluation of quantified Boolean formulas (QBFs) remains PSPACE-complete even on formulas of constant treewidth. Intuitively, this is because ordinary treewidth does not take into account the prefix of the QBF: it neither distinguishes between existential and universal variables, nor accounts for the order in which they are quantified. In the past, several weaker variants of treewidth have been devised to incorporate prefix-sensitive information. To establish tractability for QBFs under these notions, prior work has employed either strategy- or resolution-based techniques, thereby dividing the parameterized complexity landscape of QBF into two regimes that are incomparable in strength. We establish fixed-parameter tractability with respect to bilateral treewidth, a novel and strictly more powerful decompositional parameter that combines these rivaling approaches by simultaneously allowing for branching on strategies and performing Q-resolution. As in previous works in this direction, our algorithm assumes that a suitable tree decomposition is provided on the input.
Cite as

Robert Ganian and Marlene Gründel. Bilateral Treewidth for QBF: Where Strategies and Resolution Meet. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.SAT.2026.16,
  author =	{Ganian, Robert and Gr\"{u}ndel, Marlene},
  title =	{{Bilateral Treewidth for QBF: Where Strategies and Resolution Meet}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{16:1--16:20},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-263227},
  doi =		{10.4230/LIPIcs.SAT.2026.16},
  annote =	{Keywords: QBF, Treewidth, Fixed Parameter Tractability, Dependency Schemes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.38
Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees

Authors: Narek Bojikian, Alexander Firbas, Robert Ganian, Hung P. Hoang, and Krisztina Szilágyi

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

Abstract
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph G and a constraint function D, we ask for a (minimum-cost) spanning tree T such that for each vertex v, T achieves a degree specified by D(v). Specifically, we consider three kinds of constraint functions ordered by their generality - D may either assign to each vertex a list of admissible degrees, an upper bound on the degree, or a specific degree. Using a combination of novel techniques and state-of-the-art machinery, we obtain an almost-complete overview of the fine-grained complexity of these problems taking into account the most classical structural graph parameters of the input graph G. In particular, we present SETH-tight upper and lower bounds for these problems when parameterized by pathwidth and cutwidth, an ETH-tight algorithm parameterized by clique-width, and a nearly SETH-tight algorithm parameterized by treewidth. In order to obtain our upper bound for clique-width, we develop a novel technique of double representation through "requirement shifting". Using this technique, we also obtain an ETH-tight single-exponential XP algorithm for the Exact Leaf Spanning Tree problem parameterized by clique-width, which settles the final remaining open case for clique-width from the classical Cut and Count of Cygan et al. [FOCS 2011, TALG 2022]. This shows the versatility of our technique and its potential applicability to other problems as well. Additionally, in order to establish our lower and upper bounds we introduce a number of tools which may be of independent interest, including lazy coloring and "asymptotic" SETH-based reductions for structural parameters.
Cite as

Narek Bojikian, Alexander Firbas, Robert Ganian, Hung P. Hoang, and Krisztina Szilágyi. Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bojikian_et_al:LIPIcs.ICALP.2026.38,
  author =	{Bojikian, Narek and Firbas, Alexander and Ganian, Robert and Hoang, Hung P. and Szil\'{a}gyi, Krisztina},
  title =	{{Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{38:1--38:14},
  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.2026.38},
  URN =		{urn:nbn:de:0030-drops-264272},
  doi =		{10.4230/LIPIcs.ICALP.2026.38},
  annote =	{Keywords: Parameterized complexity, Structural parameters, Clique-width, fine-grained complexity, Spanning tree}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.75
Coordinated Motion Planning Is FPT on Discretized Simple Polygons

Authors: Argyrios Deligkas, Eduard Eiben, Robert Ganian, and Iyad Kanj

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

Abstract
In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of k robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two robots collide. The goal is to compute a schedule that routes all robots to their destinations while minimizing some objective function. In this paper, we focus on the well-studied objective of minimizing the total travel length of all robots. This problem is known to be NP-hard, and it has been shown to be fixed-parameter tractable (FPT), when parameterized by the number k of robots, on full grids (SoCG 2023) and on bounded-treewidth graphs (ICALP 2024). We present a fixed-parameter algorithm for coordinated motion planning, parameterized by the number k of robots, on graphs arising from discretizations of simple polygons. Such graphs are of particular interest in real-world applications, where planar motion is often constrained to discretized representations of polygonal environments. Moreover, these graphs generalize rectangular grids; consequently, our result constitutes a significant step toward resolving the parameterized complexity of coordinated motion planning on subgrids and, ultimately, planar graphs - two prominent open problems in the field.
Cite as

Argyrios Deligkas, Eduard Eiben, Robert Ganian, and Iyad Kanj. Coordinated Motion Planning Is FPT on Discretized Simple Polygons. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 75:1-75:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deligkas_et_al:LIPIcs.ICALP.2026.75,
  author =	{Deligkas, Argyrios and Eiben, Eduard and Ganian, Robert and Kanj, Iyad},
  title =	{{Coordinated Motion Planning Is FPT on Discretized Simple Polygons}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{75:1--75:13},
  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.2026.75},
  URN =		{urn:nbn:de:0030-drops-264648},
  doi =		{10.4230/LIPIcs.ICALP.2026.75},
  annote =	{Keywords: coordinated motion planning, multi-agent path finding, parameterized complexity}
}
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.SoCG.2026.36
Upward Book Embeddings of Partitioned Digraphs

Authors: Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a topological order and the edges are partitioned into pages, so that no two edges in the same page cross. For a partitioned digraph G = (V, ⋃^k_{i=1} E_i), that is, a digraph whose edge set is partitioned into k subsets, an upward book embedding is required to assign edges to pages as prescribed by the given partition. In a companion paper, Heath and Pemmaraju [SIAM J. Comput. 28(5), 1999] proved that the problem of testing the existence of an upward book embedding of a partitioned digraph is linear-time solvable for k = 1 and recently Akitaya, Demaine, Hesterberg, and Liu [GD, 2017] have shown the problem NP-complete for k ≥ 3. In this paper, we study upward book embeddings of partitioned digraphs and focus on the unsolved case k = 2. Our first main result is a novel characterization of the upward embeddings that support an upward book embedding in two pages. We exploit this characterization in several ways, and obtain a rich picture of the complexity landscape of the problem. First, we show that the problem remains NP-complete when k = 2, thus closing the complexity gap for the problem. Second, we show that, for an n-vertex partitioned digraph with a prescribed planar embedding, the existence of an upward book embedding that respects the given planar embedding can be tested in O(n log³ n) time. Finally, leveraging the SPQ(R)-tree decomposition of biconnected graphs into triconnected components, we present a cubic-time testing algorithm for biconnected directed partial 2-trees.
Cite as

Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter. Upward Book Embeddings of Partitioned Digraphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dalozzo_et_al:LIPIcs.SoCG.2026.36,
  author =	{Da Lozzo, Giordano and Frati, Fabrizio and Rutter, Ignaz},
  title =	{{Upward Book Embeddings of Partitioned Digraphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36},
  URN =		{urn:nbn:de:0030-drops-258424},
  doi =		{10.4230/LIPIcs.SoCG.2026.36},
  annote =	{Keywords: upward book embeddings, partitioned digraphs, SPQ-trees, 2-trees}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.19
Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level

Authors: Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang

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

Abstract
ARRIVAL is the problem of deciding whether a token, following a deterministic process, eventually reaches a designated destination. While the problem is known to lie in NP ∩ CoNP, whether it can be solved in polynomial time remains a major open question. In this article, we study ladders, a class of graphs that constitutes a family of worst-case instances for many existing algorithms, including the currently best known algorithm by Gärtner, Haslebacher, and Hoang (ICALP 2021). We show that ARRIVAL restricted to ladders can be solved in polynomial time, and we further extend this result to stopping binary simple stochastic games (SSG).
Cite as

Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang. Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gartner_et_al:LIPIcs.FUN.2026.19,
  author =	{G\"{a}rtner, Bernd and Haslebacher, Sebastian and Hoang, Hung P.},
  title =	{{Sinks and Ladders: ARRIVAL and SSG with Two Vertices per Level}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{19:1--19:16},
  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.2026.19},
  URN =		{urn:nbn:de:0030-drops-257385},
  doi =		{10.4230/LIPIcs.FUN.2026.19},
  annote =	{Keywords: ARRIVAL, Rotor-Routing, Simple Stochastic Games}
}
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.
Cite as

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.2026.51
Structural Parameterization of Steiner Tree Packing

Authors: Niko Hastrich and Kirill Simonov

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

Abstract
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms. In this paper, we show the first FPT algorithms for STP parameterized by structural parameters of the input graph. In particular, we show that STP is fixed-parameter tractable by the tree-cut width as well as the fracture number of the input graph. To achieve our results, we generalize techniques from Edge-Disjoint Paths (EDP) to Generalized Steiner Tree Packing (GSTP), which generalizes both STP and EDP. First, we derive the notion of the augmented graph for GSTP analogous to EDP. We then show that GSTP is FPT by - the tree-cut width of the augmented graph, - the fracture number of the augmented graph, - the slim tree-cut width of the input graph. The latter two results were previously known for EDP; our results generalize these to GSTP and improve the running time for the parameter fracture number. On the other hand, it was open whether EDP is FPT parameterized by the tree-cut width of the augmented graph, despite extensive research on the structural complexity of the problem. We settle this question affirmatively.
Cite as

Niko Hastrich and Kirill Simonov. Structural Parameterization of Steiner Tree Packing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hastrich_et_al:LIPIcs.STACS.2026.51,
  author =	{Hastrich, Niko and Simonov, Kirill},
  title =	{{Structural Parameterization of Steiner Tree Packing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{51:1--51:18},
  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.2026.51},
  URN =		{urn:nbn:de:0030-drops-255405},
  doi =		{10.4230/LIPIcs.STACS.2026.51},
  annote =	{Keywords: Steiner tree packing, structural parameters, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.41
Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide

Authors: Fatemeh Ghasemi, Julien Grange, Mamadou Moustapha Kanté, and Florent Madelaine

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
In this work we take a step towards characterising strongly flip-flat classes of graphs. Strong flip-flatness appears to be the analogue of uniform almost-wideness in the setting of dense classes of graphs. We prove that strongly flip-flat classes of graphs that are weakly sparse are indeed uniformly almost-wide.
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Fatemeh Ghasemi, Julien Grange, Mamadou Moustapha Kanté, and Florent Madelaine. Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghasemi_et_al:LIPIcs.CSL.2026.41,
  author =	{Ghasemi, Fatemeh and Grange, Julien and Kant\'{e}, Mamadou Moustapha and Madelaine, Florent},
  title =	{{Weakly-Sparse and Strongly Flip-Flat Classes of Graphs Are Uniformly Almost-Wide}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.41},
  URN =		{urn:nbn:de:0030-drops-254668},
  doi =		{10.4230/LIPIcs.CSL.2026.41},
  annote =	{Keywords: Almost-wide, Flip-flatness}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.36
A Game for Counting Logic Formula Size and an Application to Linear Orders

Authors: Grégoire Fournier and György Turán

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Ehrenfeucht-Fraïssé (EF) games are a basic tool in finite model theory for proving definability lower bounds, with many applications in complexity theory and related areas. They have been applied to study various logics, giving insights on quantifier rank and other logical complexity measures. In this paper, we present an EF game to capture formula size in counting logic with a bounded number of variables. The game combines games introduced previously for counting logic quantifier rank due to Immerman and Lander, and for first-order formula size due to Adler and Immerman, and Hella and Väänänen. The game is used to prove an extension of a formula size lower bound of Grohe and Schweikardt for distinguishing linear orders, from 3-variable first-order logic to 3-variable counting logic.
Cite as

Grégoire Fournier and György Turán. A Game for Counting Logic Formula Size and an Application to Linear Orders. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fournier_et_al:LIPIcs.CSL.2026.36,
  author =	{Fournier, Gr\'{e}goire and Tur\'{a}n, Gy\"{o}rgy},
  title =	{{A Game for Counting Logic Formula Size and an Application to Linear Orders}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.36},
  URN =		{urn:nbn:de:0030-drops-254612},
  doi =		{10.4230/LIPIcs.CSL.2026.36},
  annote =	{Keywords: Finite Model Theory, Logical Aspects of Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.66
A Parameterized-Complexity Framework for Finding Local Optima

Authors: Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm problem, introduced by Johnson, Papadimitriou, and Yannakakis (1988) fail to capture the methodology of local search algorithms: PLS is concerned with finding a local optimum and not with using local search, while the standard algorithm problem restricts each improvement step to follow a fixed pivoting rule. In this work, we introduce a novel formulation of local search which provides a middle ground between these models. In particular, the task is to output not only a local optimum but also a chain of local improvements leading to it. With this framework, we aim to capture the challenge in designing a good pivoting rule. Especially, when combined with the parameterized complexity paradigm, it enables both strong lower bounds and meaningful tractability results. Unlike previous works that combined parameterized complexity with local search, our framework targets the whole task of finding a local optimum and not only a single improvement step. Focusing on two representative meta-problems - Subset Weight Optimization Problem with the c-swap neighborhood and Weighted Circuit with the flip neighborhood - we establish fixed-parameter tractability results related to the number of distinct weights, while ruling out an analogous result when parameterizing by the distance to the nearest optimum via a new type of reduction.
Cite as

Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz. A Parameterized-Complexity Framework for Finding Local Optima. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 66:1-66:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.ITCS.2026.66,
  author =	{Ganian, Robert and Hoang, Hung P. and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Parameterized-Complexity Framework for Finding Local Optima}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{66:1--66:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.66},
  URN =		{urn:nbn:de:0030-drops-253532},
  doi =		{10.4230/LIPIcs.ITCS.2026.66},
  annote =	{Keywords: Local Search, Parameterized Complexity, PLS}
}
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.2025.31
Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard

Authors: Benjamin Bergougnoux and Lars Jaffke

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

Abstract
We prove that Hamiltonian Path and Hamiltonian Cycle are NP-hard on graphs of linear mim-width 26, even when a linear order of the input graph with mim-width 26 is provided together with input. This fills a gap left by a broken proof of the para-NP-hardness of Hamiltonicity problems parameterized by mim-width.
Cite as

Benjamin Bergougnoux and Lars Jaffke. Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 31:1-31:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergougnoux_et_al:LIPIcs.IPEC.2025.31,
  author =	{Bergougnoux, Benjamin and Jaffke, Lars},
  title =	{{Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{31:1--31:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.31},
  URN =		{urn:nbn:de:0030-drops-251631},
  doi =		{10.4230/LIPIcs.IPEC.2025.31},
  annote =	{Keywords: Hamiltonian Path, Hamiltonian Cycle, Mim-Width, Para-NP-Hardness}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.5
Kernelization for H-Coloring

Authors: Yael Berkman and Ishay Haviv

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

Abstract
For a fixed graph H, the H-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of H. A seminal theorem of Hell and Nešetřil asserts that the H-Coloring problem is NP-hard whenever H is loopless and non-bipartite. A result of Jansen and Pieterse implies that for every graph H, the H-Coloring problem parameterized by the vertex cover number k admits a kernel with O(k^Δ(H)) vertices and bit-size bounded by O(k^Δ(H)⋅log k), where Δ(H) denotes the maximum degree in H. For the case where H is a complete graph on at least three vertices, this kernel size nearly matches conditional lower bounds established by Jansen and Kratsch and by Jansen and Pieterse. This paper presents new upper and lower bounds on the kernel size of H-Coloring problems parameterized by the vertex cover number. The upper bounds arise from two kernelization algorithms. The first is purely combinatorial, and its size is governed by a structural quantity of the graph H, called the non-adjacency witness number. As applications, we obtain kernels whose size is bounded by a fixed polynomial for natural classes of graphs H with unbounded maximum degree, such as planar graphs and, more broadly, graphs with bounded degeneracy. More strikingly, we show that for almost every graph H, the degree of the polynomial that bounds the size of our combinatorial kernel grows only logarithmically in Δ(H). Our second kernel leverages linear-algebraic tools and involves the notion of faithful independent representations of graphs. It strengthens the general bound from prior work and, among other applications, yields near-optimal kernels for problems concerning the dimension of orthogonal graph representations over finite fields. We complement our kernelization results with conditional lower bounds, thereby nearly settling the kernel complexity of the problem for various target graphs H.
Cite as

Yael Berkman and Ishay Haviv. Kernelization for H-Coloring. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berkman_et_al:LIPIcs.IPEC.2025.5,
  author =	{Berkman, Yael and Haviv, Ishay},
  title =	{{Kernelization for H-Coloring}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.5},
  URN =		{urn:nbn:de:0030-drops-251376},
  doi =		{10.4230/LIPIcs.IPEC.2025.5},
  annote =	{Keywords: Kernelization, Graph coloring, Graph homomorphism}
}
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