130 Search Results for "Pilipczuk, Michał"

Volume

LIPIcs, Volume 115

13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

IPEC 2018, August 20-24, 2018, Helsinki, Finland

Editors: Christophe Paul and Michal Pilipczuk

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.17
Invariants for One-Counter Automata with Disequality Tests

Authors: Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, and Nicolas Waldburger

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study the reachability problem for one-counter automata in which transitions can carry disequality tests. A disequality test is a guard that prohibits a specified counter value. This reachability problem has been known to be NP-hard and in PSPACE, and characterising its computational complexity has been left as a challenging open question by Almagor, Cohen, Pérez, Shirmohammadi, and Worrell (2020). We reduce the complexity gap, placing the problem into the second level of the polynomial hierarchy, namely into the class coNP^NP. In the presence of both equality and disequality tests, our upper bound is at the third level, P^NP^NP. To prove this result, we show that non-reachability can be witnessed by a pair of invariants (forward and backward). These invariants are almost inductive. They aim to over-approximate only a "core" of the reachability set instead of the entire set. The invariants are also leaky: it is possible to escape the set. We complement this with separate checks as the leaks can only occur in a controlled way.
Cite as

Dmitry Chistikov, Jérôme Leroux, Henry Sinclair-Banks, and Nicolas Waldburger. Invariants for One-Counter Automata with Disequality Tests. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chistikov_et_al:LIPIcs.CONCUR.2024.17,
  author =	{Chistikov, Dmitry and Leroux, J\'{e}r\^{o}me and Sinclair-Banks, Henry and Waldburger, Nicolas},
  title =	{{Invariants for One-Counter Automata with Disequality Tests}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.17},
  URN =		{urn:nbn:de:0030-drops-207898},
  doi =		{10.4230/LIPIcs.CONCUR.2024.17},
  annote =	{Keywords: Inductive invariant, Vector addition system, One-counter automaton}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.18
Weighted Basic Parallel Processes and Combinatorial Enumeration

Authors: Lorenzo Clemente

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP equivalence problem. While (unweighted) BPP language equivalence is undecidable, we can use this algorithm to decide multiplicity equivalence of BPP and language equivalence of unambiguous BPP, with the same complexity. These are long-standing open problems for the related model of weighted context-free grammars. Our second contribution is a connection between WBPP, power series solutions of systems of polynomial differential equations, and combinatorial enumeration. To this end we consider constructible differentially finite power series (CDF), a class of multivariate differentially algebraic series introduced by Bergeron and Reutenauer in order to provide a combinatorial interpretation to differential equations. CDF series generalise rational, algebraic, and a large class of D-finite (holonomic) series, for which no complexity upper bound for equivalence was known. We show that CDF series correspond to commutative WBPP series. As a consequence of our result on WBPP and commutativity, we show that equivalence of CDF power series can be decided with 2-EXPTIME complexity. In order to showcase the CDF equivalence algorithm, we show that CDF power series naturally arise from combinatorial enumeration, namely as the exponential generating series of constructible species of structures. Examples of such species include sequences, binary trees, ordered trees, Cayley trees, set partitions, series-parallel graphs, and many others. As a consequence of this connection, we obtain an algorithm to decide multiplicity equivalence of constructible species, decidability of which was not known before. The complexity analysis is based on effective bounds from algebraic geometry, namely on the length of chains of polynomial ideals constructed by repeated application of finitely many, not necessarily commuting derivations of a multivariate polynomial ring. This is obtained by generalising a result of Novikov and Yakovenko in the case of a single derivation, which is noteworthy since generic bounds on ideal chains are non-primitive recursive in general. On the way, we develop the theory of WBPP series and CDF power series, exposing several of their appealing properties.
Cite as

Lorenzo Clemente. Weighted Basic Parallel Processes and Combinatorial Enumeration. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{clemente:LIPIcs.CONCUR.2024.18,
  author =	{Clemente, Lorenzo},
  title =	{{Weighted Basic Parallel Processes and Combinatorial Enumeration}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.18},
  URN =		{urn:nbn:de:0030-drops-207903},
  doi =		{10.4230/LIPIcs.CONCUR.2024.18},
  annote =	{Keywords: weighted automata, combinatorial enumeration, shuffle, algebraic differential equations, process algebra, basic parallel processes, species of structures}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.2
On the Complexity of the Median and Closest Permutation Problems

Authors: Luís Cunha, Ignasi Sau, and Uéverton Souza

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
Genome rearrangements are events where large blocks of DNA exchange places during evolution. The analysis of these events is a promising tool for understanding evolutionary genomics, providing data for phylogenetic reconstruction based on genome rearrangement measures. Many pairwise rearrangement distances have been proposed, based on finding the minimum number of rearrangement events to transform one genome into the other, using some predefined operation. When more than two genomes are considered, we have the more challenging problem of rearrangement-based phylogeny reconstruction. Given a set of genomes and a distance notion, there are at least two natural ways to define the "target" genome. On the one hand, finding a genome that minimizes the sum of the distances from this to any other, called the median genome. On the other hand, finding a genome that minimizes the maximum distance to any other, called the closest genome. Considering genomes as permutations of distinct integers, some distance metrics have been extensively studied. We investigate the median and closest problems on permutations over the following metrics: breakpoint distance, swap distance, block-interchange distance, short-block-move distance, and transposition distance. In biological applications some values are usually very small, such as the solution value d or the number k of input permutations. For each of these metrics and parameters d or k, we analyze the closest and the median problems from the viewpoint of parameterized complexity. We obtain the following results: NP-hardness for finding the median/closest permutation regarding some metrics of distance, even for only k = 3 permutations; Polynomial kernels for the problems of finding the median permutation of all studied metrics, considering the target distance d as parameter; NP-hardness result for finding the closest permutation by short-block-moves; FPT algorithms and infeasibility of polynomial kernels for finding the closest permutation for some metrics when parameterized by the target distance d.
Cite as

Luís Cunha, Ignasi Sau, and Uéverton Souza. On the Complexity of the Median and Closest Permutation Problems. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cunha_et_al:LIPIcs.WABI.2024.2,
  author =	{Cunha, Lu{\'\i}s and Sau, Ignasi and Souza, U\'{e}verton},
  title =	{{On the Complexity of the Median and Closest Permutation Problems}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.2},
  URN =		{urn:nbn:de:0030-drops-206468},
  doi =		{10.4230/LIPIcs.WABI.2024.2},
  annote =	{Keywords: Median problem, Closest problem, Genome rearrangements, Parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.11
Switching Classes: Characterization and Computation

Authors: Dhanyamol Antony, Yixin Cao, Sagartanu Pal, and R. B. Sandeep

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class 𝒢, we are concerned with the maximum subclass and the minimum superclass of 𝒢 that are closed under switching. We characterize the maximum subclass for many important classes 𝒢, and prove that it is finite when 𝒢 is minor-closed and omits at least one graph. For several graph classes, we develop polynomial-time algorithms to recognize the minimum superclass. We also show that the recognition of the superclass is NP-hard for H-free graphs when H is a sufficiently long path or cycle, and it cannot be solved in subexponential time assuming the Exponential Time Hypothesis.
Cite as

Dhanyamol Antony, Yixin Cao, Sagartanu Pal, and R. B. Sandeep. Switching Classes: Characterization and Computation. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{antony_et_al:LIPIcs.MFCS.2024.11,
  author =	{Antony, Dhanyamol and Cao, Yixin and Pal, Sagartanu and Sandeep, R. B.},
  title =	{{Switching Classes: Characterization and Computation}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.11},
  URN =		{urn:nbn:de:0030-drops-205678},
  doi =		{10.4230/LIPIcs.MFCS.2024.11},
  annote =	{Keywords: Switching, Graph modification, Minor-closed graph class, Hereditary graph class}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.15
Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs

Authors: Tian Bai and Mingyu Xiao

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
The Subset Feedback Vertex Set problem (SFVS) is to delete k vertices from a given graph such that in the remaining graph, any vertex in a subset T of vertices (called a terminal set) is not in a cycle. The famous Feedback Vertex Set problem is the special case of SFVS with T being the whole set of vertices. In this paper, we study exact algorithms for SFVS in Split Graphs (SFVS-S) and SFVS in Chordal Graphs (SFVS-C). SFVS-S generalizes the minimum vertex cover problem and the prize-collecting version of the maximum independent set problem in hypergraphs (PCMIS), and SFVS-C further generalizes SFVS-S. Both SFVS-S and SFVS-C are implicit 3-Hitting Set problems. However, it is not easy to solve them faster than 3-Hitting Set. In 2019, Philip, Rajan, Saurabh, and Tale (Algorithmica 2019) proved that SFVS-C can be solved in 𝒪^*(2^k) time, slightly improving the best result 𝒪^*(2.0755^k) for 3-Hitting Set. In this paper, we break the "2^k-barrier" for SFVS-S and SFVS-C by introducing an 𝒪^*(1.8192^k)-time algorithm. This achievement also indicates that PCMIS can be solved in 𝒪^*(1.8192ⁿ) time, marking the first exact algorithm for PCMIS that outperforms the trivial 𝒪^*(2ⁿ) threshold. Our algorithm uses reduction and branching rules based on the Dulmage-Mendelsohn decomposition and a divide-and-conquer method.
Cite as

Tian Bai and Mingyu Xiao. Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bai_et_al:LIPIcs.MFCS.2024.15,
  author =	{Bai, Tian and Xiao, Mingyu},
  title =	{{Breaking the Barrier 2^k for Subset Feedback Vertex Set in Chordal Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.15},
  URN =		{urn:nbn:de:0030-drops-205711},
  doi =		{10.4230/LIPIcs.MFCS.2024.15},
  annote =	{Keywords: Subset Feedback Vertex Set, Prize-Collecting Maximum Independent Set, Parameterized Algorithms, Split Graphs, Chordal Graphs, Dulmage-Mendelsohn Decomposition}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.16
Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints

Authors: Susobhan Bandopadhyay, Aritra Banik, Diptapriyo Majumdar, and Abhishek Sahu

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given an undirected graph G and a set A ⊆ V(G), an A-path is a path in G that starts and ends at two distinct vertices of A with intermediate vertices in V(G)⧵A. An A-path is called an (A,𝓁)-path if the length of the path is exactly 𝓁. In the (A, 𝓁)-Path Packing problem (ALPP), we seek to determine whether there exist k vertex-disjoint (A, 𝓁)-paths in G or not. The problem is already known to be fixed-parmeter tractable when parameterized by k+𝓁 via color coding while it remains Para-NP-hard when parameterized by k (Hamiltonian Path) or 𝓁 (P₃-Partition) alone. Therefore, a logical direction to pursue this problem is to examine it in relation to structural parameters. Belmonte et al. initiated a study along these lines and proved that ALPP parameterized by pw+|A| is W[1]-hard where pw is the pathwidth of G. In this paper, we strengthen their result and prove that it is unlikely that ALPP is fixed-parameter tractable even with respect to a bigger parameter (|A|+dtp) where dtp denotes the distance between G and a path graph (distance to path). We use a randomized reduction to achieve the mentioned result. Toward this, we prove a lemma similar to the influential "isolation lemma": Given a set system (X,ℱ) if the elements of X are assigned a weight uniformly at random from a set of values fairly large, then each subset in ℱ will have a unique weight with high probability. We believe that this result will be useful beyond the scope of this paper. ALPP being hard even for structural parameters like distance to path+|A| rules out the possibility of any FPT algorithms for many well-known other structural parameters, including FVS+|A| and treewidth+|A|. There is a straightforward FPT algorithm for ALPP parameterized by vc, the vertex cover number of the input graph. Following this, we consider the parameters CVD(cluster vertex deletion)+|A| and CVD+|𝓁| and show the problem to be FPT with respect to these parameters. Note that CVD is incomparable to the treewidth of a graph and has been in vogue recently.
Cite as

Susobhan Bandopadhyay, Aritra Banik, Diptapriyo Majumdar, and Abhishek Sahu. Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bandopadhyay_et_al:LIPIcs.MFCS.2024.16,
  author =	{Bandopadhyay, Susobhan and Banik, Aritra and Majumdar, Diptapriyo and Sahu, Abhishek},
  title =	{{Tractability of Packing Vertex-Disjoint A-Paths Under Length Constraints}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.16},
  URN =		{urn:nbn:de:0030-drops-205725},
  doi =		{10.4230/LIPIcs.MFCS.2024.16},
  annote =	{Keywords: Parameterized complexity, (A,𝓁)-Path Packing, Kernelization, Randomized-Exponential Time Hypothesis, Graph Classes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.17
On the Descriptive Complexity of Vertex Deletion Problems

Authors: Max Bannach, Florian Chudigiewitsch, and Till Tantau

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property. Regarding k as the parameter, a dichotomy was recently shown based on the number of quantifier alternations of first-order formulas that describe the property. In this paper, we refine this classification by moving from quantifier alternations to individual quantifier patterns and from a dichotomy to a trichotomy, resulting in a complete classification of the complexity of vertex deletion problems based on their quantifier pattern. The more fine-grained approach uncovers new tractable fragments, which we show to not only lie in FPT, but even in parameterized constant-depth circuit complexity classes. On the other hand, we show that vertex deletion becomes intractable already for just one quantifier per alternation, that is, there is a formula of the form ∀ x∃ y∀ z (ψ), with ψ quantifier-free, for which the vertex deletion problem is W[1]-hard. The fine-grained analysis also allows us to uncover differences in the complexity landscape when we consider different kinds of graphs and more general structures: While basic graphs (undirected graphs without self-loops), undirected graphs, and directed graphs each have a different frontier of tractability, the frontier for arbitrary logical structures coincides with that of directed graphs.
Cite as

Max Bannach, Florian Chudigiewitsch, and Till Tantau. On the Descriptive Complexity of Vertex Deletion Problems. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bannach_et_al:LIPIcs.MFCS.2024.17,
  author =	{Bannach, Max and Chudigiewitsch, Florian and Tantau, Till},
  title =	{{On the Descriptive Complexity of Vertex Deletion Problems}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.17},
  URN =		{urn:nbn:de:0030-drops-205733},
  doi =		{10.4230/LIPIcs.MFCS.2024.17},
  annote =	{Keywords: graph problems, fixed-parameter tractability, descriptive complexity, vertex deletion}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.22
Graph Search Trees and the Intermezzo Problem

Authors: Jesse Beisegel, Ekkehard Köhler, Fabienne Ratajczak, Robert Scheffler, and Martin Strehler

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
The last in-tree recognition problem asks whether a given spanning tree can be derived by connecting each vertex with its rightmost left neighbor of some search ordering. In this study, we demonstrate that the last-in-tree recognition problem for Generic Search is NP-complete. We utilize this finding to strengthen a complexity result from order theory. Given a partial order π and a set of triples, the NP-complete intermezzo problem asks for a linear extension of π where each first element of a triple is not between the other two. We show that this problem remains NP-complete even when the Hasse diagram of the partial order forms a tree of bounded height. In contrast, we give an XP-algorithm for the problem when parameterized by the width of the partial order. Furthermore, we show that - under the assumption of the Exponential Time Hypothesis - the running time of this algorithm is asymptotically optimal.
Cite as

Jesse Beisegel, Ekkehard Köhler, Fabienne Ratajczak, Robert Scheffler, and Martin Strehler. Graph Search Trees and the Intermezzo Problem. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beisegel_et_al:LIPIcs.MFCS.2024.22,
  author =	{Beisegel, Jesse and K\"{o}hler, Ekkehard and Ratajczak, Fabienne and Scheffler, Robert and Strehler, Martin},
  title =	{{Graph Search Trees and the Intermezzo Problem}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.22},
  URN =		{urn:nbn:de:0030-drops-205781},
  doi =		{10.4230/LIPIcs.MFCS.2024.22},
  annote =	{Keywords: graph search trees, intermezzo problem, algorithm, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.24
Breaking a Graph into Connected Components with Small Dominating Sets

Authors: Matthias Bentert, Michael R. Fellows, Petr A. Golovach, Frances A. Rosamond, and Saket Saurabh

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We study DOMINATED CLUSTER DELETION. Therein, we are given an undirected graph G = (V,E) and integers k and d and the task is to find a set of at most k vertices such that removing these vertices results in a graph in which each connected component has a dominating set of size at most d. We also consider the special case where d is a constant. We show an almost complete tetrachotomy in terms of para-NP-hardness, containment in XP, containment in FPT, and admitting a polynomial kernel with respect to parameterizations that are a combination of k,d,c, and Δ, where c and Δ are the degeneracy and the maximum degree of the input graph, respectively. As a main contribution, we show that the problem can be solved in f(k,d) ⋅ n^O(d) time, that is, the problem is FPT when parameterized by k when d is a constant. This answers an open problem asked in a recent Dagstuhl seminar (23331). For the special case d = 1, we provide an algorithm with running time 2^𝒪(klog k) nm. Furthermore, we show that even for d = 1, the problem does not admit a polynomial kernel with respect to k + c.
Cite as

Matthias Bentert, Michael R. Fellows, Petr A. Golovach, Frances A. Rosamond, and Saket Saurabh. Breaking a Graph into Connected Components with Small Dominating Sets. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bentert_et_al:LIPIcs.MFCS.2024.24,
  author =	{Bentert, Matthias and Fellows, Michael R. and Golovach, Petr A. and Rosamond, Frances A. and Saurabh, Saket},
  title =	{{Breaking a Graph into Connected Components with Small Dominating Sets}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.24},
  URN =		{urn:nbn:de:0030-drops-205801},
  doi =		{10.4230/LIPIcs.MFCS.2024.24},
  annote =	{Keywords: Parameterized Algorithms, Recursive Understanding, Polynomial Kernels, Degeneracy}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.29
Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra

Authors: Václav Blažej, Dušan Knop, Jan Pokorný, and Šimon Schierreich

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In the Equitable Connected Partition (ECP for short) problem, we are given a graph G = (V,E) together with an integer p ∈ ℕ, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G and the size of each two parts differs by at most 1. On the one hand, the problem is known to be NP-hard in general and W[1]-hard with respect to the path-width, the feedback-vertex set, and the number of parts p combined. On the other hand, fixed-parameter algorithms are known for parameters the vertex-integrity and the max leaf number. In this work, we systematically study ECP with respect to various structural restrictions of the underlying graph and provide a clear dichotomy of its parameterised complexity. Specifically, we show that the problem is in FPT when parameterized by the modular-width and the distance to clique. Next, we prove W[1]-hardness with respect to the distance to cluster, the 4-path vertex cover number, the distance to disjoint paths, and the feedback-edge set, and NP-hardness for constant shrub-depth graphs. Our hardness results are complemented by matching algorithmic upper-bounds: we give an XP algorithm for parameterisation by the tree-width and the distance to cluster. We also give an improved FPT algorithm for parameterisation by the vertex integrity and the first explicit FPT algorithm for the 3-path vertex cover number. The main ingredient of these algorithms is a formulation of ECP as N-fold IP, which clearly indicates that such formulations may, in certain scenarios, significantly outperform existing algorithms based on the famous algorithm of Lenstra.
Cite as

Václav Blažej, Dušan Knop, Jan Pokorný, and Šimon Schierreich. Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{blazej_et_al:LIPIcs.MFCS.2024.29,
  author =	{Bla\v{z}ej, V\'{a}clav and Knop, Du\v{s}an and Pokorn\'{y}, Jan and Schierreich, \v{S}imon},
  title =	{{Equitable Connected Partition and Structural Parameters Revisited: N-Fold Beats Lenstra}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.29},
  URN =		{urn:nbn:de:0030-drops-205857},
  doi =		{10.4230/LIPIcs.MFCS.2024.29},
  annote =	{Keywords: Equitable Connected Partition, structural parameters, fixed-parameter tractability, N-fold integer programming, tree-width, shrub-depth, modular-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.32
Symmetric-Difference (Degeneracy) and Signed Tree Models

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We introduce a dense counterpart of graph degeneracy, which extends the recently-proposed invariant symmetric difference. We say that a graph has sd-degeneracy (for symmetric-difference degeneracy) at most d if it admits an elimination order of its vertices where a vertex u can be removed whenever it has a d-twin, i.e., another vertex v such that at most d vertices outside {u,v} are neighbors of exactly one of u, v. The family of graph classes of bounded sd-degeneracy is a superset of that of graph classes of bounded degeneracy or of bounded flip-width, and more generally, of bounded symmetric difference. Unlike most graph parameters, sd-degeneracy is not hereditary: it may be strictly smaller on a graph than on some of its induced subgraphs. In particular, every n-vertex graph is an induced subgraph of some O(n²)-vertex graph of sd-degeneracy 1. In spite of this and the breadth of classes of bounded sd-degeneracy, we devise Õ(√n)-bit adjacency labeling schemes for them, which are optimal up to the hidden polylogarithmic factor. This is attained on some even more general classes, consisting of graphs G whose vertices bijectively map to the leaves of a tree T, where transversal edges and anti-edges added to T define the edge set of G. We call such graph representations signed tree models as they extend the so-called tree models (or twin-decompositions) developed in the context of twin-width, by adding transversal anti-edges. While computing the degeneracy of a graph takes linear time, we show that determining its symmetric difference is para-co-NP-complete. This may seem surprising as symmetric difference can serve as a short-sighted first approximation of twin-width, whose computation is para-NP-complete. Indeed, we show that deciding if the symmetric difference of an input graph is at most 8 is co-NP-complete. We also show that deciding if the sd-degeneracy is at most 6 is NP-complete, contrasting with the symmetric difference.
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Symmetric-Difference (Degeneracy) and Signed Tree Models. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonnet_et_al:LIPIcs.MFCS.2024.32,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Symmetric-Difference (Degeneracy) and Signed Tree Models}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.32},
  URN =		{urn:nbn:de:0030-drops-205886},
  doi =		{10.4230/LIPIcs.MFCS.2024.32},
  annote =	{Keywords: symmetric difference, degeneracy, adjacency labeling schemes, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.36
Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs

Authors: Arnaud Casteigts, Nils Morawietz, and Petra Wolf

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither symmetric nor transitive, the latter having important consequences on the computational complexity of even basic questions, such as computing temporal connected components. In this paper, we introduce several parameters that capture how far a temporal graph 𝒢 is from being transitive, namely, vertex-deletion distance to transitivity and arc-modification distance to transitivity, both being applied to the reachability graph of 𝒢. We illustrate the impact of these parameters on the temporal connected component problem, obtaining several tractability results in terms of fixed-parameter tractability and polynomial kernels. Significantly, these results are obtained without restrictions of the underlying graph, the snapshots, or the lifetime of the input graph. As such, our results isolate the impact of non-transitivity and confirm the key role that it plays in the hardness of temporal graph problems.
Cite as

Arnaud Casteigts, Nils Morawietz, and Petra Wolf. Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{casteigts_et_al:LIPIcs.MFCS.2024.36,
  author =	{Casteigts, Arnaud and Morawietz, Nils and Wolf, Petra},
  title =	{{Distance to Transitivity: New Parameters for Taming Reachability in Temporal Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.36},
  URN =		{urn:nbn:de:0030-drops-205923},
  doi =		{10.4230/LIPIcs.MFCS.2024.36},
  annote =	{Keywords: Temporal graphs, Parameterized complexity, Reachability, Transitivity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.38
Algorithms and Complexity for Path Covers of Temporal DAGs

Authors: Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A path cover of a digraph is a collection of paths collectively containing its vertex set. A path cover with minimum cardinality for a directed acyclic graph can be found in polynomial time [Fulkerson, AMS'56; Cáceres et al., SODA'22]. Moreover, Dilworth’s celebrated theorem on chain coverings of partially ordered sets equivalently states that the minimum size of a path cover of a DAG is equal to the maximum size of a set of mutually unreachable vertices. In this paper, we examine how far these classic results can be extended to a dynamic setting. A temporal digraph has an arc set that changes over discrete time-steps; if the underlying digraph is acyclic, then it is a temporal DAG. A temporal path is a directed path in the underlying digraph, such that the time-steps of arcs are strictly increasing along the path. Two temporal paths are temporally disjoint if they do not occupy any vertex at the same time. A temporal path cover is a collection 𝒞 of temporal paths that covers all vertices, and 𝒞 is temporally disjoint if all its temporal paths are pairwise temporally disjoint. We study the computational complexities of the problems of finding a minimum-size temporal (disjoint) path cover (denoted as Temporal Path Cover and Temporally Disjoint Path Cover). On the negative side, we show that both Temporal Path Cover and Temporally Disjoint Path Cover are NP-hard even when the underlying DAG is planar, bipartite, subcubic, and there are only two arc-disjoint time-steps. Moreover, Temporally Disjoint Path Cover remains NP-hard even on temporal oriented trees. We also observe that natural temporal analogues of Dilworth’s theorem on these classes of temporal DAGs do not hold. In contrast, we show that Temporal Path Cover is polynomial-time solvable on temporal oriented trees by a reduction to Clique Cover for (static undirected) weakly chordal graphs (a subclass of perfect graphs for which Clique Cover admits an efficient algorithm). This highlights an interesting algorithmic difference between the two problems. Although it is NP-hard on temporal oriented trees, Temporally Disjoint Path Cover becomes polynomial-time solvable on temporal oriented lines and temporal rooted directed trees. Motivated by the hardness result on trees, we show that, in contrast, Temporal Path Cover admits an XP time algorithm with respect to parameter t_max + tw, where t_max is the maximum time-step and tw is the treewidth of the underlying static undirected graph; moreover, Temporally Disjoint Path Cover admits an FPT algorithm with respect to the same parameterization.
Cite as

Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing. Algorithms and Complexity for Path Covers of Temporal DAGs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2024.38,
  author =	{Chakraborty, Dibyayan and Dailly, Antoine and Foucaud, Florent and Klasing, Ralf},
  title =	{{Algorithms and Complexity for Path Covers of Temporal DAGs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.38},
  URN =		{urn:nbn:de:0030-drops-205940},
  doi =		{10.4230/LIPIcs.MFCS.2024.38},
  annote =	{Keywords: Temporal Graphs, Dilworth’s Theorem, DAGs, Path Cover, Temporally Disjoint Paths, Algorithms, Oriented Trees, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.43
The Even-Path Problem in Directed Single-Crossing-Minor-Free Graphs

Authors: Archit Chauhan, Samir Datta, Chetan Gupta, and Vimal Raj Sharma

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Finding a simple path of even length between two designated vertices in a directed graph is a fundamental NP-complete problem [Andrea S. LaPaugh and Christos H. Papadimitriou, 1984] known as the EP problem. Nedev [Zhivko Prodanov Nedev, 1999] proved in 1999, that for directed planar graphs, the problem can be solved in polynomial time. More than two decades since then, we make the first progress in extending the tractable classes of graphs for this problem. We give a polynomial time algorithm to solve the EP problem for classes of H-minor-free directed graphs, where H is a single-crossing graph. We make two new technical contributions along the way, that might be of independent interest. The first, and perhaps our main, contribution is the construction of small, planar, parity-mimicking networks. These are graphs that mimic parities of all possible paths between a designated set of terminals of the original graph. Finding vertex disjoint paths between given source-destination pairs of vertices is another fundamental problem, known to be NP-complete in directed graphs [Steven Fortune et al., 1980], though known to be tractable in planar directed graphs [Alexander Schrijver, 1994]. We encounter a natural variant of this problem, that of finding disjoint paths between given pairs of vertices, but with constraints on parity of the total length of paths. The other significant contribution of our paper is to give a polynomial time algorithm for the 3-disjoint paths with total parity problem, in directed planar graphs with some restrictions (and also in directed graphs of bounded treewidth).
Cite as

Archit Chauhan, Samir Datta, Chetan Gupta, and Vimal Raj Sharma. The Even-Path Problem in Directed Single-Crossing-Minor-Free Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chauhan_et_al:LIPIcs.MFCS.2024.43,
  author =	{Chauhan, Archit and Datta, Samir and Gupta, Chetan and Sharma, Vimal Raj},
  title =	{{The Even-Path Problem in Directed Single-Crossing-Minor-Free Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.43},
  URN =		{urn:nbn:de:0030-drops-205992},
  doi =		{10.4230/LIPIcs.MFCS.2024.43},
  annote =	{Keywords: Graph Algorithms, EvenPath, Polynomial-time Algorithms, Reachability}
}
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