9 Search Results for "Katsikarelis, Ioannis"

Document
DOI: 10.4230/LIPIcs.ESA.2024.39
List Homomorphisms by Deleting Edges and Vertices: Tight Complexity Bounds for Bounded-Treewidth Graphs

Authors: Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The goal of this paper is to investigate a family of optimization problems arising from list homomorphisms, and to understand what the best possible algorithms are if we restrict the problem to bounded-treewidth graphs. Given graphs G, H, and lists L(v) ⊆ V(H) for every v ∈ V(G), a list homomorphism from (G,L) to H is a function f:V(G) → V(H) that preserves the edges (i.e., uv ∈ E(G) implies f(u)f(v) ∈ E(H)) and respects the lists (i.e., f(v) ∈ L(v)). The graph H may have loops. For a fixed H, the input of the optimization problem LHomVD(H) is a graph G with lists L(v), and the task is to find a set X of vertices having minimum size such that (G-X,L) has a list homomorphism to H. We define analogously the edge-deletion variant LHomED(H), where we have to delete as few edges as possible from G to obtain a graph that has a list homomorphism. This expressive family of problems includes members that are essentially equivalent to fundamental problems such as Vertex Cover, Max Cut, Odd Cycle Transversal, and Edge/Vertex Multiway Cut. For both variants, we first characterize those graphs H that make the problem polynomial-time solvable and show that the problem is NP-hard for every other fixed H. Second, as our main result, we determine for every graph H for which the problem is NP-hard, the smallest possible constant c_H such that the problem can be solved in time c^t_H⋅ n^{𝒪(1)} if a tree decomposition of G having width t is given in the input. Let i(H) be the maximum size of a set of vertices in H that have pairwise incomparable neighborhoods. For the vertex-deletion variant LHomVD(H), we show that the smallest possible constant is i(H)+1 for every H: - Given a tree decomposition of width t of G, LHomVD(H) can be solved in time (i(H)+1)^t⋅ n^{𝒪(1)}. - For any ε > 0 and H, an (i(H)+1-ε)^t⋅ n^{𝒪(1)} algorithm would violate the Strong Exponential-Time Hypothesis (SETH). The situation is more complex for the edge-deletion version. For every H, one can solve LHomED(H) in time i(H)^t⋅ n^{𝒪(1)} if a tree decomposition of width t is given. However, the existence of a specific type of decomposition of H shows that there are graphs H where LHomED(H) can be solved significantly more efficiently and the best possible constant can be arbitrarily smaller than i(H). Nevertheless, we determine this best possible constant and (assuming the SETH) prove tight bounds for every fixed H.
Cite as

Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski. List Homomorphisms by Deleting Edges and Vertices: Tight Complexity Bounds for Bounded-Treewidth Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{canesmer_et_al:LIPIcs.ESA.2024.39,
  author =	{Can Esmer, Bar{\i}\c{s} and Focke, Jacob and Marx, D\'{a}niel and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{List Homomorphisms by Deleting Edges and Vertices: Tight Complexity Bounds for Bounded-Treewidth Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.39},
  URN =		{urn:nbn:de:0030-drops-211103},
  doi =		{10.4230/LIPIcs.ESA.2024.39},
  annote =	{Keywords: Graph Homomorphism, List Homomorphism, Vertex Deletion, Edge Deletion, Multiway Cut, Parameterized Complexity, Tight Bounds, Treewidth, SETH}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.55
Hitting Meets Packing: How Hard Can It Be?

Authors: Jacob Focke, Fabian Frei, Shaohua Li, Dániel Marx, Philipp Schepper, Roohani Sharma, and Karol Węgrzycki

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of 𝒳-HitPack asks: Can removing k (deletable) vertices of a graph G prevent us from packing 𝓁 vertex-disjoint objects of type 𝒳? This problem captures a spectrum of problems with standard hitting and packing on opposite ends. Our main motivating question is whether the combination 𝒳-HitPack can be significantly harder than these two base problems. Already for one particular choice of 𝒳, this question can be posed for many different complexity notions, leading to a large, so-far unexplored domain at the intersection of the areas of hitting and packing problems. At a high level, we present two case studies: (1) 𝒳 being all cycles, and (2) 𝒳 being all copies of a fixed graph H. In each, we explore the classical complexity as well as the parameterized complexity with the natural parameters k+𝓁 and treewidth. We observe that the combined problem can be drastically harder than the base problems: for cycles or for H being a connected graph on at least 3 vertices, the problem is Σ₂^𝖯-complete and requires double-exponential dependence on the treewidth of the graph (assuming the Exponential-Time Hypothesis). In contrast, the combined problem admits qualitatively similar running times as the base problems in some cases, although significant novel ideas are required. For 𝒳 being all cycles, we establish a 2^{poly(k+𝓁)}⋅ n^{𝒪(1)} algorithm using an involved branching method, for example. Also, for 𝒳 being all edges (i.e., H = K₂; this combines Vertex Cover and Maximum Matching) the problem can be solved in time 2^{poly(tw)}⋅ n^{𝒪(1)} on graphs of treewidth tw. The key step enabling this running time relies on a combinatorial bound obtained from an algebraic (linear delta-matroid) representation of possible matchings.
Cite as

Jacob Focke, Fabian Frei, Shaohua Li, Dániel Marx, Philipp Schepper, Roohani Sharma, and Karol Węgrzycki. Hitting Meets Packing: How Hard Can It Be?. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 55:1-55:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{focke_et_al:LIPIcs.ESA.2024.55,
  author =	{Focke, Jacob and Frei, Fabian and Li, Shaohua and Marx, D\'{a}niel and Schepper, Philipp and Sharma, Roohani and W\k{e}grzycki, Karol},
  title =	{{Hitting Meets Packing: How Hard Can It Be?}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{55:1--55:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.55},
  URN =		{urn:nbn:de:0030-drops-211261},
  doi =		{10.4230/LIPIcs.ESA.2024.55},
  annote =	{Keywords: Hitting, Packing, Covering, Parameterized Algorithms, Lower Bounds, Treewidth}
}
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.2024.29
A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

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

Abstract
Given a graph G = (V,E), a set T ⊆ V, and an integer b, the Steiner Tree problem asks whether G has a connected subgraph H with at most b vertices that spans all of T. This work presents a 3^k⋅ n^𝒪(1) time one-sided Monte-Carlo algorithm for solving Steiner Tree when additionally a clique-expression of width k is provided. Known lower bounds for less expressive parameters imply that this dependence on the clique-width of G is optimal assuming the Strong Exponential-Time Hypothesis (SETH). Indeed our work establishes that the parameter dependence of Steiner Tree is the same for any graph parameter between cutwidth and clique-width, assuming SETH. Our work contributes to the program of determining the exact parameterized complexity of fundamental hard problems relative to structural graph parameters such as treewidth, which was initiated by Lokshtanov et al. [SODA 2011 & TALG 2018] and which by now has seen a plethora of results. Since the cut-and-count framework of Cygan et al. [FOCS 2011 & TALG 2022], connectivity problems have played a key role in this program as they pose many challenges for developing tight upper and lower bounds. Recently, Hegerfeld and Kratsch [ESA 2023] gave the first application of the cut-and-count technique to problems parameterized by clique-width and obtained tight bounds for Connected Dominating Set and Connected Vertex Cover, leaving open the complexity of other benchmark connectivity problems such as Steiner Tree and Feedback Vertex Set. Our algorithm for Steiner Tree does not follow the cut-and-count technique and instead works with the connectivity patterns of partial solutions. As a first technical contribution we identify a special family of so-called complete patterns that has strong (existential) representation properties, and using these at least one solution will be preserved. Furthermore, there is a family of 3^k basis patterns that (parity) represents the complete patterns, i.e., it has the same number of solutions modulo two. Our main technical contribution, a new technique called "isolating a representative," allows us to leverage both forms of representation (existential and parity). Both complete patterns and isolation of a representative will likely be applicable to other (connectivity) problems.
Cite as

Narek Bojikian and Stefan Kratsch. A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bojikian_et_al:LIPIcs.ICALP.2024.29,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{29:1--29:18},
  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.2024.29},
  URN =		{urn:nbn:de:0030-drops-201728},
  doi =		{10.4230/LIPIcs.ICALP.2024.29},
  annote =	{Keywords: Parameterized complexity, Steiner tree, clique-width}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.34
Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness

Authors: Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski

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

Abstract
It is known for many algorithmic problems that if a tree decomposition of width t is given in the input, then the problem can be solved with exponential dependence on t. A line of research initiated by Lokshtanov, Marx, and Saurabh [SODA 2011] produced lower bounds showing that in many cases known algorithms already achieve the best possible exponential dependence on t, assuming the Strong Exponential-Time Hypothesis (SETH). The main message of this paper is showing that the same lower bounds can already be obtained in a much more restricted setting: informally, a graph consisting of a block of t vertices connected to components of constant size already has the same hardness as a general tree decomposition of width t. Formally, a (σ,δ)-hub is a set Q of vertices such that every component of Q has size at most σ and is adjacent to at most δ vertices of Q. We explore if the known tight lower bounds parameterized by the width of the given tree decomposition remain valid if we parameterize by the size of the given hub. - For every ε > 0, there are σ,δ > 0 such that Independent Set (equivalently Vertex Cover) cannot be solved in time (2-ε)^p⋅ n, even if a (σ, δ)-hub of size p is given in the input, assuming the SETH. This matches the earlier tight lower bounds parameterized by width of the tree decomposition. Similar tight bounds are obtained for Odd Cycle Transversal, Max Cut, q-Coloring, and edge/vertex deletions versions of q-Coloring. - For every ε > 0, there are σ,δ > 0 such that △-Partition cannot be solved in time (2-ε)^p ⋅ n, even if a (σ, δ)-hub of size p is given in the input, assuming the Set Cover Conjecture (SCC). In fact, we prove that this statement is equivalent to the SCC, thus it is unlikely that this could be proved assuming the SETH. - For Dominating Set, we can prove a non-tight lower bound ruling out (2-ε)^p ⋅ n^𝒪(1) algorithms, assuming either the SETH or the SCC, but this does not match the 3^p⋅ n^{𝒪(1)} upper bound. Thus our results reveal that, for many problems, the research on lower bounds on the dependence on tree width was never really about tree decompositions, but the real source of hardness comes from a much simpler structure. Additionally, we study if the same lower bounds can be obtained if σ and δ are fixed universal constants (not depending on ε). We show that lower bounds of this form are possible for Max Cut and the edge-deletion version of q-Coloring, under the Max 3-Sat Hypothesis (M3SH). However, no such lower bounds are possible for Independent Set, Odd Cycle Transversal, and the vertex-deletion version of q-Coloring: better than brute force algorithms are possible for every fixed (σ,δ).
Cite as

Barış Can Esmer, Jacob Focke, Dániel Marx, and Paweł Rzążewski. Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{canesmer_et_al:LIPIcs.ICALP.2024.34,
  author =	{Can Esmer, Bar{\i}\c{s} and Focke, Jacob and Marx, D\'{a}niel and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{34:1--34:17},
  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.2024.34},
  URN =		{urn:nbn:de:0030-drops-201772},
  doi =		{10.4230/LIPIcs.ICALP.2024.34},
  annote =	{Keywords: Parameterized Complexity, Tight Bounds, Hub, Treewidth, Strong Exponential Time Hypothesis, Vertex Coloring, Vertex Deletion, Edge Deletion, Triangle Packing, Triangle Partition, Set Cover Hypothesis, Dominating Set}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.77
Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters

Authors: Carla Groenland, Isja Mannens, Jesper Nederlof, Marta Piecyk, and Paweł Rzążewski

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

Abstract
A homomorphism from a graph G to a graph H is an edge-preserving mapping from V(G) to V(H). In the graph homomorphism problem, denoted by Hom(H), the graph H is fixed and we need to determine if there exists a homomorphism from an instance graph G to H. We study the complexity of the problem parameterized by the cutwidth of G, i.e., we assume that G is given along with a linear ordering v_1,…,v_n of V(G) such that, for each i ∈ {1,…,n-1}, the number of edges with one endpoint in {v_1,…,v_i} and the other in {v_{i+1},…,v_n} is at most k. We aim, for each H, for algorithms for Hom(H) running in time c_H^k n^𝒪(1) and matching lower bounds that exclude c_H^{k⋅o(1)} n^𝒪(1) or c_H^{k(1-Ω(1))} n^𝒪(1) time algorithms under the (Strong) Exponential Time Hypothesis. In the paper we introduce a new parameter that we call mimsup(H). Our main contribution is strong evidence of a close connection between c_H and mimsup(H): - an information-theoretic argument that the number of states needed in a natural dynamic programming algorithm is at most mimsup(H)^k, - lower bounds that show that for almost all graphs H indeed we have c_H ≥ mimsup(H), assuming the (Strong) Exponential-Time Hypothesis, and - an algorithm with running time exp(𝒪(mimsup(H)⋅k log k)) n^𝒪(1). In the last result we do not need to assume that H is a fixed graph. Thus, as a consequence, we obtain that the problem of deciding whether G admits a homomorphism to H is fixed-parameter tractable, when parameterized by cutwidth of G and mimsup(H). The parameter mimsup(H) can be thought of as the p-th root of the maximum induced matching number in the graph obtained by multiplying p copies of H via a certain graph product, where p tends to infinity. It can also be defined as an asymptotic rank parameter of the adjacency matrix of H. Such parameters play a central role in, among others, algebraic complexity theory and additive combinatorics. Our results tightly link the parameterized complexity of a problem to such an asymptotic matrix parameter for the first time.
Cite as

Carla Groenland, Isja Mannens, Jesper Nederlof, Marta Piecyk, and Paweł Rzążewski. Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 77:1-77:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{groenland_et_al:LIPIcs.ICALP.2024.77,
  author =	{Groenland, Carla and Mannens, Isja and Nederlof, Jesper and Piecyk, Marta and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{Towards Tight Bounds for the Graph Homomorphism Problem Parameterized by Cutwidth via Asymptotic Matrix Parameters}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{77:1--77:21},
  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.2024.77},
  URN =		{urn:nbn:de:0030-drops-202208},
  doi =		{10.4230/LIPIcs.ICALP.2024.77},
  annote =	{Keywords: graph homomorphism, cutwidth, asymptotic matrix parameters}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.67
New Results on Directed Edge Dominating Set

Authors: Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Eun Jung Kim, and Michael Lampis

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We study a family of generalizations of Edge Dominating Set on directed graphs called Directed (p,q)-Edge Dominating Set. In this problem an arc (u,v) is said to dominate itself, as well as all arcs which are at distance at most q from v, or at distance at most p to u. First, we give significantly improved FPT algorithms for the two most important cases of the problem, (0,1)-dEDS and (1,1)-dEDS (that correspond to versions of Dominating Set on line graphs), as well as polynomial kernels. We also improve the best-known approximation for these cases from logarithmic to constant. In addition, we show that (p,q)-dEDS is FPT parameterized by p+q+tw, but W-hard parameterized just by tw, where tw is the treewidth of the underlying graph of the input. We then go on to focus on the complexity of the problem on tournaments. Here, we provide a complete classification for every possible fixed value of p,q, which shows that the problem exhibits a surprising behavior, including cases which are in P; cases which are solvable in quasi-polynomial time but not in P; and a single case (p=q=1) which is NP-hard (under randomized reductions) and cannot be solved in sub-exponential time, under standard assumptions.
Cite as

Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Eun Jung Kim, and Michael Lampis. New Results on Directed Edge Dominating Set. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 67:1-67:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{belmonte_et_al:LIPIcs.MFCS.2018.67,
  author =	{Belmonte, R\'{e}my and Hanaka, Tesshu and Katsikarelis, Ioannis and Kim, Eun Jung and Lampis, Michael},
  title =	{{New Results on Directed Edge Dominating Set}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{67:1--67:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul 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.MFCS.2018.67},
  URN =		{urn:nbn:de:0030-drops-96490},
  doi =		{10.4230/LIPIcs.MFCS.2018.67},
  annote =	{Keywords: Edge Dominating Set, Tournaments, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2018.24
Parameterized Orientable Deletion

Authors: Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Yota Otachi, and Florian Sikora

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Abstract
A graph is d-orientable if its edges can be oriented so that the maximum in-degree of the resulting digraph is at most d. d-orientability is a well-studied concept with close connections to fundamental graph-theoretic notions and applications as a load balancing problem. In this paper we consider the d-Orientable Deletion problem: given a graph G=(V,E), delete the minimum number of vertices to make G d-orientable. We contribute a number of results that improve the state of the art on this problem. Specifically: - We show that the problem is W[2]-hard and log n-inapproximable with respect to k, the number of deleted vertices. This closes the gap in the problem's approximability. - We completely characterize the parameterized complexity of the problem on chordal graphs: it is FPT parameterized by d+k, but W-hard for each of the parameters d,k separately. - We show that, under the SETH, for all d,epsilon, the problem does not admit a (d+2-epsilon)^{tw}, algorithm where tw is the graph's treewidth, resolving as a special case an open problem on the complexity of PseudoForest Deletion. - We show that the problem is W-hard parameterized by the input graph's clique-width. Complementing this, we provide an algorithm running in time d^{O(d * cw)}, showing that the problem is FPT by d+cw, and improving the previously best know algorithm for this case.
Cite as

Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Yota Otachi, and Florian Sikora. Parameterized Orientable Deletion. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hanaka_et_al:LIPIcs.SWAT.2018.24,
  author =	{Hanaka, Tesshu and Katsikarelis, Ioannis and Lampis, Michael and Otachi, Yota and Sikora, Florian},
  title =	{{Parameterized Orientable Deletion}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.24},
  URN =		{urn:nbn:de:0030-drops-88506},
  doi =		{10.4230/LIPIcs.SWAT.2018.24},
  annote =	{Keywords: Graph orientations, FPT algorithms, Treewidth, SETH}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.50
Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center

Authors: Ioannis Katsikarelis, Michael Lampis, and Vangelis Th. Paschos

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
In (k,r)-Center we are given a (possibly edge-weighted) graph and are asked to select at most k vertices (centers), so that all other vertices are at distance at most r from a center. In this paper we provide a number of tight fine-grained bounds on the complexity of this problem with respect to various standard graph parameters. Specifically: - For any r>=1, we show an algorithm that solves the problem in O*((3r+1)^cw) time, where cw is the clique-width of the input graph, as well as a tight SETH lower bound matching this algorithm's performance. As a corollary, for r=1, this closes the gap that previously existed on the complexity of Dominating Set parameterized by cw. - We strengthen previously known FPT lower bounds, by showing that (k,r)-Center is W[1]-hard parameterized by the input graph's vertex cover (if edge weights are allowed), or feedback vertex set, even if k is an additional parameter. Our reductions imply tight ETH-based lower bounds. Finally, we devise an algorithm parameterized by vertex cover for unweighted graphs. - We show that the complexity of the problem parameterized by tree-depth is 2^Theta(td^2) by showing an algorithm of this complexity and a tight ETH-based lower bound. We complement these mostly negative results by providing FPT approximation schemes parameterized by clique-width or treewidth which work efficiently independently of the values of k,r. In particular, we give algorithms which, for any epsilon>0, run in time O*((tw/epsilon)^O(tw)), O*((cw/epsilon)^O(cw)) and return a (k,(1+epsilon)r)-center, if a (k,r)-center exists, thus circumventing the problem's W-hardness.
Cite as

Ioannis Katsikarelis, Michael Lampis, and Vangelis Th. Paschos. Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{katsikarelis_et_al:LIPIcs.ISAAC.2017.50,
  author =	{Katsikarelis, Ioannis and Lampis, Michael and Paschos, Vangelis Th.},
  title =	{{Structural Parameters, Tight Bounds, and Approximation for (k,r)-Center}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{50:1--50:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.50},
  URN =		{urn:nbn:de:0030-drops-82441},
  doi =		{10.4230/LIPIcs.ISAAC.2017.50},
  annote =	{Keywords: FPT algorithms, Approximation, Treewidth, Clique-width, Domination}
}
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