32 Search Results for "Lampis, Michael"

Document
DOI: 10.4230/LIPIcs.ISAAC.2024.39
Core Stability in Additively Separable Hedonic Games of Low Treewidth

Authors: Tesshu Hanaka, Noleen Köhler, and Michael Lampis

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
Additively Separable Hedonic Games (ASHGs) are coalition-formation games where we are given a directed graph whose vertices represent n selfish agents and the weight of each arc uv denotes the preferences from u to v. We revisit the computational complexity of the well-known notion of core stability of symmetric ASHGs, where the goal is to construct a partition of the agents into coalitions such that no group of agents would prefer to diverge from the given partition and form a new coalition. For Core Stability Verification (CSV), we first show the following hardness results: CSV remains coNP-complete on graphs of vertex cover 2; CSV is coW[1]-hard parameterized by vertex integrity when edge weights are polynomially bounded; and CSV is coW[1]-hard parameterized by tree-depth even if all weights are from {-1,1}. We complement these results with essentially matching algorithms and color{black}{an FPT algorithm parameterized by the treewidth tw plus the maximum degree Δ (improving a previous algorithm’s dependence from 2^O(twΔ²)} to 2^O(twΔ)).} We then move on to study Core Stability (CS), which one would naturally expect to be even harder than CSV. We confirm this intuition by showing that CS is Σ₂^p-complete even on graphs of bounded vertex cover number. On the positive side, we present a 2^{2^O(Δtw)}n^O(1)-time algorithm parameterized by tw+Δ, which is essentially optimal assuming Exponential Time Hypothesis (ETH). Finally, we consider the notion of k-core stability: k denotes the maximum size of the allowed blocking (diverging) coalitions. We show that k-CSV is coW[1]-hard parameterized by k (even on unweighted graphs), while k-CS is NP-complete for all k ≥ 3 (even on graphs of bounded degree with bounded edge weights).
Cite as

Tesshu Hanaka, Noleen Köhler, and Michael Lampis. Core Stability in Additively Separable Hedonic Games of Low Treewidth. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2024.39,
  author =	{Hanaka, Tesshu and K\"{o}hler, Noleen and Lampis, Michael},
  title =	{{Core Stability in Additively Separable Hedonic Games of Low Treewidth}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.39},
  URN =		{urn:nbn:de:0030-drops-221662},
  doi =		{10.4230/LIPIcs.ISAAC.2024.39},
  annote =	{Keywords: Hedonic games, Treewidth, Core stability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.58
Parameterized Vertex Integrity Revisited

Authors: Tesshu Hanaka, Michael Lampis, Manolis Vasilakis, and Kanae Yoshiwatari

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

Abstract
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components which are themselves also small. Graphs with low vertex integrity are very structured; this renders many hard problems tractable and has recently attracted interest in this notion from the parameterized complexity community. In this paper we revisit the NP-complete problem of computing the vertex integrity of a given graph from the point of view of structural parameterizations. We present a number of new results, which also answer some recently posed open questions from the literature. Specifically, we show that unweighted vertex integrity is W[1]-hard parameterized by treedepth; we show that the problem remains W[1]-hard if we parameterize by feedback edge set size (via a reduction from a Bin Packing variant which may be of independent interest); and complementing this we show that the problem is FPT by max-leaf number. Furthermore, for weighted vertex integrity, we show that the problem admits a single-exponential FPT algorithm parameterized by vertex cover or by modular width, the latter result improving upon a previous algorithm which required weights to be polynomially bounded.
Cite as

Tesshu Hanaka, Michael Lampis, Manolis Vasilakis, and Kanae Yoshiwatari. Parameterized Vertex Integrity Revisited. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hanaka_et_al:LIPIcs.MFCS.2024.58,
  author =	{Hanaka, Tesshu and Lampis, Michael and Vasilakis, Manolis and Yoshiwatari, Kanae},
  title =	{{Parameterized Vertex Integrity Revisited}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{58:1--58:14},
  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.2024.58},
  URN =		{urn:nbn:de:0030-drops-206141},
  doi =		{10.4230/LIPIcs.MFCS.2024.58},
  annote =	{Keywords: Parameterized Complexity, Treedepth, Vertex Integrity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.61
Parameterized Algorithms for Steiner Forest in Bounded Width Graphs

Authors: Andreas Emil Feldmann and Michael Lampis

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and the aim is to find a minimum cost subgraph in which each given vertex pair lies in the same connected component. It is known that this problem is APX-hard in general, and NP-hard on graphs of treewidth 3, treedepth 4, and feedback vertex set size 2. However, Bateni, Hajiaghayi and Marx [JACM, 2011] gave an approximation scheme with a runtime of n^O(k²/ε) on graphs of treewidth k. Our main result is a much faster efficient parameterized approximation scheme (EPAS) with a runtime of 2^O(k²/ε log k/ε)⋅n^O(1). If k instead is the vertex cover number of the input graph, we show how to compute the optimum solution in 2^O(k log k)⋅n^O(1) time, and we also prove that this runtime dependence on k is asymptotically best possible, under ETH. Furthermore, if k is the size of a feedback edge set, then we obtain a faster 2^O(k)⋅n^O(1) time algorithm, which again cannot be improved under ETH.
Cite as

Andreas Emil Feldmann and Michael Lampis. Parameterized Algorithms for Steiner Forest in Bounded Width Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 61:1-61:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{feldmann_et_al:LIPIcs.ICALP.2024.61,
  author =	{Feldmann, Andreas Emil and Lampis, Michael},
  title =	{{Parameterized Algorithms for Steiner Forest in Bounded Width Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{61:1--61:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.61},
  URN =		{urn:nbn:de:0030-drops-202048},
  doi =		{10.4230/LIPIcs.ICALP.2024.61},
  annote =	{Keywords: Steiner Forest, Approximation Algorithms, FPT algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.77
Structural Parameterizations for Two Bounded Degree Problems Revisited

Authors: Michael Lampis and Manolis Vasilakis

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph G and a target degree Δ and we are asked either to edit or partition the graph so that the maximum degree becomes bounded by Δ. Both problems are known to be parameterized intractable for the most well-known structural parameters, such as treewidth. We revisit the parameterization by treewidth, as well as several related parameters and present a more fine-grained picture of the complexity of both problems. In particular: - Both problems admit straightforward DP algorithms with table sizes (Δ+2)^tw and (χ_d(Δ+1))^{tw} respectively, where tw is the input graph’s treewidth and χ_d the number of available colors. We show that, under the SETH, both algorithms are essentially optimal, for any non-trivial fixed values of Δ, χ_d, even if we replace treewidth by pathwidth. Along the way, we obtain an algorithm for Defective Coloring with complexity quasi-linear in the table size, thus settling the complexity of both problems for treewidth and pathwidth. - Given that the standard DP algorithm is optimal for treewidth and pathwidth, we then go on to consider the more restricted parameter tree-depth. Here, previously known lower bounds imply that, under the ETH, Bounded Vertex Degree Deletion and Defective Coloring cannot be solved in time n^o(∜{td}) and n^o(√{td}) respectively, leaving some hope that a qualitatively faster algorithm than the one for treewidth may be possible. We close this gap by showing that neither problem can be solved in time n^o(td), under the ETH, by employing a recursive low tree-depth construction that may be of independent interest. - Finally, we consider a structural parameter that is known to be restrictive enough to render both problems FPT: vertex cover. For both problems the best known algorithm in this setting has a super-exponential dependence of the form vc^𝒪(vc). We show that this is optimal, as an algorithm with dependence of the form vc^o(vc) would violate the ETH. Our proof relies on a new application of the technique of d-detecting families introduced by Bonamy et al. [ToCT 2019]. Our results, although mostly negative in nature, paint a clear picture regarding the complexity of both problems in the landscape of parameterized complexity, since in all cases we provide essentially matching upper and lower bounds.
Cite as

Michael Lampis and Manolis Vasilakis. Structural Parameterizations for Two Bounded Degree Problems Revisited. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 77:1-77:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lampis_et_al:LIPIcs.ESA.2023.77,
  author =	{Lampis, Michael and Vasilakis, Manolis},
  title =	{{Structural Parameterizations for Two Bounded Degree Problems Revisited}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{77:1--77:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.77},
  URN =		{urn:nbn:de:0030-drops-187302},
  doi =		{10.4230/LIPIcs.ESA.2023.77},
  annote =	{Keywords: ETH, Parameterized Complexity, SETH}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.62
Parameterized Max Min Feedback Vertex Set

Authors: Michael Lampis, Nikolaos Melissinos, and Manolis Vasilakis

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).
Cite as

Michael Lampis, Nikolaos Melissinos, and Manolis Vasilakis. Parameterized Max Min Feedback Vertex Set. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lampis_et_al:LIPIcs.MFCS.2023.62,
  author =	{Lampis, Michael and Melissinos, Nikolaos and Vasilakis, Manolis},
  title =	{{Parameterized Max Min Feedback Vertex Set}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.62},
  URN =		{urn:nbn:de:0030-drops-185965},
  doi =		{10.4230/LIPIcs.MFCS.2023.62},
  annote =	{Keywords: ETH, Feedback vertex set, Parameterized algorithms, Treewidth}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.132
First Order Logic on Pathwidth Revisited Again

Authors: Michael Lampis

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Courcelle’s celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height increases with each quantifier alternation in the formula. More devastatingly, this cannot be improved, under standard assumptions, even if we consider the much more restricted problem of deciding FO-expressible properties on trees. In this paper we revisit this well-studied topic and identify a natural special case where the dependence of Courcelle’s theorem can, in fact, be improved. Specifically, we show that all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth). This is a rare example of treewidth and pathwidth having different complexity behaviors. Our result is also in sharp contrast with MSO logic on graphs of bounded pathwidth, where it is known that the dependence has to be non-elementary, under standard assumptions. Our work builds upon, and generalizes, a corresponding meta-theorem by Gajarský and Hliněný for the more restricted class of graphs of bounded tree-depth.
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Michael Lampis. First Order Logic on Pathwidth Revisited Again. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 132:1-132:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lampis:LIPIcs.ICALP.2023.132,
  author =	{Lampis, Michael},
  title =	{{First Order Logic on Pathwidth Revisited Again}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{132:1--132:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.132},
  URN =		{urn:nbn:de:0030-drops-181848},
  doi =		{10.4230/LIPIcs.ICALP.2023.132},
  annote =	{Keywords: Algorithmic Meta-Theorems, FO logic, Pathwidth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.20
Extended MSO Model Checking via Small Vertex Integrity

Authors: Tatsuya Gima and Yota Otachi

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSO^GL_Lin, introduced recently by Knop, Koutecký, Masařík, and Toufar [Log. Methods Comput. Sci., 15(4), 2019]. We show that the problem is fixed-parameter tractable parameterized by vertex integrity, where vertex integrity is a graph parameter standing between vertex cover number and treedepth. Our result thus narrows the gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.
Cite as

Tatsuya Gima and Yota Otachi. Extended MSO Model Checking via Small Vertex Integrity. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gima_et_al:LIPIcs.ISAAC.2022.20,
  author =	{Gima, Tatsuya and Otachi, Yota},
  title =	{{Extended MSO Model Checking via Small Vertex Integrity}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.20},
  URN =		{urn:nbn:de:0030-drops-173056},
  doi =		{10.4230/LIPIcs.ISAAC.2022.20},
  annote =	{Keywords: vertex integrity, monadic second-order logic, cardinality constraint, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.64
Hedonic Games and Treewidth Revisited

Authors: Tesshu Hanaka and Michael Lampis

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an edge-weighted digraph G = (V,E), and the weight of an arc uv denotes the utility u gains by being in the same coalition as v. We focus on (arguably) the most basic stability question about such a game: given a graph, does a Nash stable solution exist and can we find it efficiently? We study the (parameterized) complexity of ASHG stability when the underlying graph has treewidth t and maximum degree Δ. The current best FPT algorithm for this case was claimed by Peters [AAAI 2016], with time complexity roughly 2^{O(Δ⁵t)}. We present an algorithm with parameter dependence (Δ t)^{O(Δ t)}, significantly improving upon the parameter dependence on Δ given by Peters, albeit with a slightly worse dependence on t. Our main result is that this slight performance deterioration with respect to t is actually completely justified: we observe that the previously claimed algorithm is incorrect, and that in fact no algorithm can achieve dependence t^{o(t)} for bounded-degree graphs, unless the ETH fails. This, together with corresponding bounds we provide on the dependence on Δ and the joint parameter establishes that our algorithm is essentially optimal for both parameters, under the ETH. We then revisit the parameterization by treewidth alone and resolve a question also posed by Peters by showing that Nash Stability remains strongly NP-hard on stars under additive preferences. Nevertheless, we also discover an island of mild tractability: we show that Connected Nash Stability is solvable in pseudo-polynomial time for constant t, though with an XP dependence on t which, as we establish, cannot be avoided.
Cite as

Tesshu Hanaka and Michael Lampis. Hedonic Games and Treewidth Revisited. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hanaka_et_al:LIPIcs.ESA.2022.64,
  author =	{Hanaka, Tesshu and Lampis, Michael},
  title =	{{Hedonic Games and Treewidth Revisited}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.64},
  URN =		{urn:nbn:de:0030-drops-170025},
  doi =		{10.4230/LIPIcs.ESA.2022.64},
  annote =	{Keywords: Hedonic Games, Nash Equilibrium, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.45
Determining a Slater Winner Is Complete for Parallel Access to NP

Authors: Michael Lampis

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We consider the complexity of deciding the winner of an election under the Slater rule. In this setting we are given a tournament T = (V,A), where the vertices of V represent candidates and the direction of each arc indicates which of the two endpoints is preferable for the majority of voters. The Slater score of a vertex v ∈ V is defined as the minimum number of arcs that need to be reversed so that T becomes acyclic and v becomes the winner. We say that v is a Slater winner in T if v has minimum Slater score in T. Deciding if a vertex is a Slater winner in a tournament has long been known to be NP-hard. However, the best known complexity upper bound for this problem is the class Θ₂^p, which corresponds to polynomial-time Turing machines with parallel access to an NP oracle. In this paper we close this gap by showing that the problem is Θ₂^p-complete, and that this hardness applies to instances constructible by aggregating the preferences of 7 voters.
Cite as

Michael Lampis. Determining a Slater Winner Is Complete for Parallel Access to NP. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 45:1-45:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lampis:LIPIcs.STACS.2022.45,
  author =	{Lampis, Michael},
  title =	{{Determining a Slater Winner Is Complete for Parallel Access to NP}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{45:1--45:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.45},
  URN =		{urn:nbn:de:0030-drops-158555},
  doi =		{10.4230/LIPIcs.STACS.2022.45},
  annote =	{Keywords: Slater winner, Feedback Arc Set, Tournaments}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.34
Fine-Grained Meta-Theorems for Vertex Integrity

Authors: Michael Lampis and Valia Mitsou

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
Vertex Integrity is a graph measure which sits squarely between two more well-studied notions, namely vertex cover and tree-depth, and that has recently gained attention as a structural graph parameter. In this paper we investigate the algorithmic trade-offs involved with this parameter from the point of view of algorithmic meta-theorems for First-Order (FO) and Monadic Second Order (MSO) logic. Our positive results are the following: (i) given a graph G of vertex integrity k and an FO formula ϕ with q quantifiers, deciding if G satisfies ϕ can be done in time 2^O(k²q + q log q) + n^O(1); (ii) for MSO formulas with q quantifiers, the same can be done in time 2^{2^O(k²+kq)} + n^O(1). Both results are obtained using kernelization arguments, which pre-process the input to sizes 2^O(k²)q and 2^O(k²+kq) respectively. The complexities of our meta-theorems are significantly better than the corresponding meta-theorems for tree-depth, which involve towers of exponentials. However, they are worse than the roughly 2^{O(kq)} and 2^{2^{O(k+q)}} complexities known for corresponding meta-theorems for vertex cover. To explain this deterioration we present two formula constructions which lead to fine-grained complexity lower bounds and establish that the dependence of our meta-theorems on k is best possible. More precisely, we show that it is not possible to decide FO formulas with q quantifiers in time 2^o(k²q), and that there exists a constant-size MSO formula which cannot be decided in time 2^{2^o(k²)}, both under the ETH. Hence, the quadratic blow-up in the dependence on k is unavoidable and vertex integrity has a complexity for FO and MSO logic which is truly intermediate between vertex cover and tree-depth.
Cite as

Michael Lampis and Valia Mitsou. Fine-Grained Meta-Theorems for Vertex Integrity. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lampis_et_al:LIPIcs.ISAAC.2021.34,
  author =	{Lampis, Michael and Mitsou, Valia},
  title =	{{Fine-Grained Meta-Theorems for Vertex Integrity}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.34},
  URN =		{urn:nbn:de:0030-drops-154674},
  doi =		{10.4230/LIPIcs.ISAAC.2021.34},
  annote =	{Keywords: Model-Checking, Fine-grained complexity, Vertex Integrity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.36
Filling Crosswords Is Very Hard

Authors: Laurent Gourvès, Ararat Harutyunyan, Michael Lampis, and Nikolaos Melissinos

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We revisit a classical crossword filling puzzle which already appeared in Garey&Jonhson’s book. We are given a grid with n vertical and horizontal slots and a dictionary with m words and are asked to place words from the dictionary in the slots so that shared cells are consistent. We attempt to pinpoint the source of intractability of this problem by carefully taking into account the structure of the grid graph, which contains a vertex for each slot and an edge if two slots intersect. Our main approach is to consider the case where this graph has a tree-like structure. Unfortunately, if we impose the common rule that words cannot be reused, we discover that the problem remains NP-hard under very severe structural restrictions, namely, if the grid graph is a union of stars and the alphabet has size 2, or the grid graph is a matching (so the crossword is a collection of disjoint crosses) and the alphabet has size 3. The problem does become slightly more tractable if word reuse is allowed, as we obtain an m^{tw} algorithm in this case, where tw is the treewidth of the grid graph. However, even in this case, we show that our algorithm cannot be improved to obtain fixed-parameter tractability. More strongly, we show that under the ETH the problem cannot be solved in time m^o(k), where k is the number of horizontal slots of the instance (which trivially bounds tw). Motivated by these mostly negative results, we also consider the much more restricted case where the problem is parameterized by the number of slots n. Here, we show that the problem does become FPT (if the alphabet has constant size), but the parameter dependence is exponential in n². We show that this dependence is also justified: the existence of an algorithm with running time 2^o(n²), even for binary alphabet, would contradict the randomized ETH. Finally, we consider an optimization version of the problem, where we seek to place as many words on the grid as possible. Here it is easy to obtain a 1/2-approximation, even on weighted instances, simply by considering only horizontal or only vertical slots. We show that this trivial algorithm is also likely to be optimal, as obtaining a better approximation ratio in polynomial time would contradict the Unique Games Conjecture. The latter two results apply whether word reuse is allowed or not.
Cite as

Laurent Gourvès, Ararat Harutyunyan, Michael Lampis, and Nikolaos Melissinos. Filling Crosswords Is Very Hard. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gourves_et_al:LIPIcs.ISAAC.2021.36,
  author =	{Gourv\`{e}s, Laurent and Harutyunyan, Ararat and Lampis, Michael and Melissinos, Nikolaos},
  title =	{{Filling Crosswords Is Very Hard}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.36},
  URN =		{urn:nbn:de:0030-drops-154690},
  doi =		{10.4230/LIPIcs.ISAAC.2021.36},
  annote =	{Keywords: Crossword Puzzle, Treewidth, ETH}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.4
A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover

Authors: Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph G and a positive integer k, and the objective is to decide whether G contains a minimal vertex cover of size at least k. Motivated by the kernelization of MMVC with parameter k, our main contribution is to introduce a simple general framework to obtain lower bounds on the degrees of a certain type of polynomial kernels for vertex-optimization problems, which we call {lop-kernels}. Informally, this type of kernels is required to preserve large optimal solutions in the reduced instance, and captures the vast majority of existing kernels in the literature. As a consequence of this framework, we show that the trivial quadratic kernel for MMVC is essentially optimal, answering a question of Boria et al. [Discret. Appl. Math. 2015], and that the known cubic kernel for Maximum Minimal Feedback Vertex Set is also essentially optimal. On the positive side, given the (plausible) non-existence of subquadratic kernels for MMVC on general graphs, we provide subquadratic kernels on H-free graphs for several graphs H, such as the bull, the paw, or the complete graphs, by making use of the Erdős-Hajnal property in order to find an appropriate decomposition. Finally, we prove that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover of the input graph, even on bipartite graphs, unless NP ⊆ coNP / poly. This indicates that parameters smaller than the solution size are unlike to yield polynomial kernels for MMVC.
Cite as

Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau. A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{araujo_et_al:LIPIcs.IPEC.2021.4,
  author =	{Ara\'{u}jo, J\'{u}lio and Bougeret, Marin and Campos, Victor and Sau, Ignasi},
  title =	{{A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.4},
  URN =		{urn:nbn:de:0030-drops-153879},
  doi =		{10.4230/LIPIcs.IPEC.2021.4},
  annote =	{Keywords: Maximum minimal vertex cover, parameterized complexity, polynomial kernel, kernelization lower bound, Erd\H{o}s-Hajnal property, induced subgraphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.92
Minimum Stable Cut and Treewidth

Authors: Michael Lampis

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. Equivalently, a cut is stable if all vertices have the (weighted) majority of their neighbors on the other side. Finding a stable cut is a prototypical PLS-complete problem that has been studied in the context of local search and of algorithmic game theory. In this paper we study Min Stable Cut, the problem of finding a stable cut of minimum weight, which is closely related to the Price of Anarchy of the Max Cut game. Since this problem is NP-hard, we study its complexity on graphs of low treewidth, low degree, or both. We begin by showing that the problem remains weakly NP-hard on severely restricted trees, so bounding treewidth alone cannot make it tractable. We match this hardness with a pseudo-polynomial DP algorithm solving the problem in time (Δ⋅ W)^{O(tw)}n^{O(1)}, where tw is the treewidth, Δ the maximum degree, and W the maximum weight. On the other hand, bounding Δ is also not enough, as the problem is NP-hard for unweighted graphs of bounded degree. We therefore parameterize Min Stable Cut by both tw and Δ and obtain an FPT algorithm running in time 2^{O(Δtw)}(n+log W)^{O(1)}. Our main result for the weighted problem is to provide a reduction showing that both aforementioned algorithms are essentially optimal, even if we replace treewidth by pathwidth: if there exists an algorithm running in (nW)^{o(pw)} or 2^{o(Δpw)}(n+log W)^{O(1)}, then the ETH is false. Complementing this, we show that we can, however, obtain an FPT approximation scheme parameterized by treewidth, if we consider almost-stable solutions, that is, solutions where no single vertex can unilaterally increase the weight of its incident cut edges by more than a factor of (1+ε). Motivated by these mostly negative results, we consider Unweighted Min Stable Cut. Here our results already imply a much faster exact algorithm running in time Δ^{O(tw)}n^{O(1)}. We show that this is also probably essentially optimal: an algorithm running in n^{o(pw)} would contradict the ETH.
Cite as

Michael Lampis. Minimum Stable Cut and Treewidth. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 92:1-92:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lampis:LIPIcs.ICALP.2021.92,
  author =	{Lampis, Michael},
  title =	{{Minimum Stable Cut and Treewidth}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{92:1--92:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.92},
  URN =		{urn:nbn:de:0030-drops-141616},
  doi =		{10.4230/LIPIcs.ICALP.2021.92},
  annote =	{Keywords: Treewidth, Local Max-Cut, Nash Stability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.41
Digraph Coloring and Distance to Acyclicity

Authors: Ararat Harutyunyan, Michael Lampis, and Nikolaos Melissinos

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
In k-Digraph Coloring we are given a digraph and are asked to partition its vertices into at most k sets, so that each set induces a DAG. This well-known problem is NP-hard, as it generalizes (undirected) k-Coloring, but becomes trivial if the input digraph is acyclic. This poses the natural parameterized complexity question of what happens when the input is "almost" acyclic. In this paper we study this question using parameters that measure the input’s distance to acyclicity in either the directed or the undirected sense. In the directed sense perhaps the most natural notion of distance to acyclicity is directed feedback vertex set (DFVS). It is already known that, for all k ≥ 2, k-Digraph Coloring is NP-hard on digraphs of DFVS at most k+4. We strengthen this result to show that, for all k ≥ 2, k-Digraph Coloring is already NP-hard for DFVS exactly k. This immediately provides a dichotomy, as k-Digraph Coloring is trivial if DFVS is at most k-1. Refining our reduction we obtain two further consequences: (i) for all k ≥ 2, k-Digraph Coloring is NP-hard for graphs of feedback arc set (FAS) at most k²; interestingly, this leads to a second dichotomy, as we show that the problem is FPT by k if FAS is at most k²-1; (ii) k-Digraph Coloring is NP-hard for graphs of DFVS k, even if the maximum degree Δ is at most 4k-1; we show that this is also almost tight, as the problem becomes FPT for DFVS k and Δ ≤ 4k-3. Since these results imply that the problem is also NP-hard on graphs of bounded directed treewidth, we then consider parameters that measure the distance from acyclicity of the underlying graph. On the positive side, we show that k-Digraph Coloring admits an FPT algorithm parameterized by treewidth, whose parameter dependence is (tw!)k^{tw}. Since this is considerably worse than the k^{tw} dependence of (undirected) k-Coloring, we pose the question of whether the tw! factor can be eliminated. Our main contribution in this part is to settle this question in the negative and show that our algorithm is essentially optimal, even for the much more restricted parameter treedepth and for k = 2. Specifically, we show that an FPT algorithm solving 2-Digraph Coloring with dependence td^o(td) would contradict the ETH.
Cite as

Ararat Harutyunyan, Michael Lampis, and Nikolaos Melissinos. Digraph Coloring and Distance to Acyclicity. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{harutyunyan_et_al:LIPIcs.STACS.2021.41,
  author =	{Harutyunyan, Ararat and Lampis, Michael and Melissinos, Nikolaos},
  title =	{{Digraph Coloring and Distance to Acyclicity}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.41},
  URN =		{urn:nbn:de:0030-drops-136865},
  doi =		{10.4230/LIPIcs.STACS.2021.41},
  annote =	{Keywords: Digraph Coloring, Dichromatic number, NP-completeness, Parameterized complexity, Feedback vertex and arc sets}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.9
New Algorithms for Mixed Dominating Set

Authors: Louis Dublois, Michael Lampis, and Vangelis Th. Paschos

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
A mixed dominating set is a set of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for MDS, resolving some open questions. In particular, we settle the problem’s complexity parameterized by treewidth and pathwidth by giving an algorithm running in time O^*(5^{tw}) (improving the current best O^*(6^{tw})), and a lower bound showing that our algorithm cannot be improved under the SETH, even if parameterized by pathwidth (improving a lower bound of O^*((2-ε)^{pw})). Furthermore, by using a simple but so far overlooked observation on the structure of minimal solutions, we obtain branching algorithms which improve the best known FPT algorithm for this problem, from O^*(4.172^k) to O^*(3.510^k), and the best known exact algorithm, from O^*(2ⁿ) and exponential space, to O^*(1.912ⁿ) and polynomial space.
Cite as

Louis Dublois, Michael Lampis, and Vangelis Th. Paschos. New Algorithms for Mixed Dominating Set. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dublois_et_al:LIPIcs.IPEC.2020.9,
  author =	{Dublois, Louis and Lampis, Michael and Paschos, Vangelis Th.},
  title =	{{New Algorithms for Mixed Dominating Set}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.9},
  URN =		{urn:nbn:de:0030-drops-133127},
  doi =		{10.4230/LIPIcs.IPEC.2020.9},
  annote =	{Keywords: FPT Algorithms, Exact Algorithms, Mixed Domination}
}
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