88 Search Results for "Fomin, Fedor"

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.32
Computing Paths of Large Rank in Planar Frameworks Deterministically

Authors: Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, and Giannos Stamoulis

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
A framework consists of an undirected graph G and a matroid M whose elements correspond to the vertices of G. Recently, Fomin et al. [SODA 2023] and Eiben et al. [ArXiV 2023] developed parameterized algorithms for computing paths of rank k in frameworks. More precisely, for vertices s and t of G, and an integer k, they gave FPT algorithms parameterized by k deciding whether there is an (s,t)-path in G whose vertex set contains a subset of elements of M of rank k. These algorithms are based on Schwartz-Zippel lemma for polynomial identity testing and thus are randomized, and therefore the existence of a deterministic FPT algorithm for this problem remains open. We present the first deterministic FPT algorithm that solves the problem in frameworks whose underlying graph G is planar. While the running time of our algorithm is worse than the running times of the recent randomized algorithms, our algorithm works on more general classes of matroids. In particular, this is the first FPT algorithm for the case when matroid M is represented over rationals. Our main technical contribution is the nontrivial adaptation of the classic irrelevant vertex technique to frameworks to reduce the given instance to one of bounded treewidth. This allows us to employ the toolbox of representative sets to design a dynamic programming procedure solving the problem efficiently on instances of bounded treewidth.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, and Giannos Stamoulis. Computing Paths of Large Rank in Planar Frameworks Deterministically. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 32:1-32:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ISAAC.2023.32,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Korhonen, Tuukka and Stamoulis, Giannos},
  title =	{{Computing Paths of Large Rank in Planar Frameworks Deterministically}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.32},
  URN =		{urn:nbn:de:0030-drops-193341},
  doi =		{10.4230/LIPIcs.ISAAC.2023.32},
  annote =	{Keywords: Planar graph, longest path, linear matroid, irrelevant vertex}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.7
Faster Detours in Undirected Graphs

Authors: Shyan Akmal, Virginia Vassilevska Williams, Ryan Williams, and Zixuan Xu

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

Abstract
The k-Detour problem is a basic path-finding problem: given a graph G on n vertices, with specified nodes s and t, and a positive integer k, the goal is to determine if G has an st-path of length exactly dist(s,t) + k, where dist(s,t) is the length of a shortest path from s to t. The k-Detour problem is NP-hard when k is part of the input, so researchers have sought efficient parameterized algorithms for this task, running in f(k)poly(n) time, for f(⋅) as slow-growing as possible. We present faster algorithms for k-Detour in undirected graphs, running in 1.853^k poly(n) randomized and 4.082^kpoly(n) deterministic time. The previous fastest algorithms for this problem took 2.746^k poly(n) randomized and 6.523^k poly(n) deterministic time [Bezáková-Curticapean-Dell-Fomin, ICALP 2017]. Our algorithms use the fact that detecting a path of a given length in an undirected graph is easier if we are promised that the path belongs to what we call a "bipartitioned" subgraph, where the nodes are split into two parts and the path must satisfy constraints on those parts. Previously, this idea was used to obtain the fastest known algorithm for finding paths of length k in undirected graphs [Björklund-Husfeldt-Kaski-Koivisto, JCSS 2017], intuitively by looking for paths of length k in randomly bipartitioned subgraphs. Our algorithms for k-Detour stem from a new application of this idea, which does not involve choosing the bipartitioned subgraphs randomly. Our work has direct implications for the k-Longest Detour problem, another related path-finding problem. In this problem, we are given the same input as in k-Detour, but are now tasked with determining if G has an st-path of length at least dist(s,t)+k. Our results for k-Detour imply that we can solve k-Longest Detour in 3.432^k poly(n) randomized and 16.661^k poly(n) deterministic time. The previous fastest algorithms for this problem took 7.539^k poly(n) randomized and 42.549^k poly(n) deterministic time [Fomin et al., STACS 2022].
Cite as

Shyan Akmal, Virginia Vassilevska Williams, Ryan Williams, and Zixuan Xu. Faster Detours in Undirected Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 7:1-7:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{akmal_et_al:LIPIcs.ESA.2023.7,
  author =	{Akmal, Shyan and Vassilevska Williams, Virginia and Williams, Ryan and Xu, Zixuan},
  title =	{{Faster Detours in Undirected Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{7:1--7:17},
  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.2023.7},
  URN =		{urn:nbn:de:0030-drops-186601},
  doi =		{10.4230/LIPIcs.ESA.2023.7},
  annote =	{Keywords: path finding, detours, parameterized complexity, exact algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.33
Polynomial-Time Approximation of Independent Set Parameterized by Treewidth

Authors: Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo

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

Abstract
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a "non-trivial" approximation ratio (as a function of the number of vertices of the input graph G) can be turned into an approximation algorithm achieving almost the same ratio, albeit as a function of the treewidth of G. More formally, we prove that for any function f, the existence of a polynomial time (n/f(n))-approximation algorithm yields the existence of a polynomial time O(tw⋅log{f(tw)}/f(tw))-approximation algorithm, where n and tw denote the number of vertices and the width of a given tree decomposition of the input graph. By pipelining our result with the state-of-the-art O(n ⋅ (log log n)²/log³n)-approximation algorithm by Feige (2004), this implies an O(tw⋅(log log tw)³/log³tw)-approximation algorithm.
Cite as

Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo. Polynomial-Time Approximation of Independent Set Parameterized by Treewidth. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 33:1-33:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chalermsook_et_al:LIPIcs.ESA.2023.33,
  author =	{Chalermsook, Parinya and Fomin, Fedor and Hamm, Thekla and Korhonen, Tuukka and Nederlof, Jesper and Orgo, Ly},
  title =	{{Polynomial-Time Approximation of Independent Set Parameterized by Treewidth}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{33:1--33:13},
  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.2023.33},
  URN =		{urn:nbn:de:0030-drops-186865},
  doi =		{10.4230/LIPIcs.ESA.2023.33},
  annote =	{Keywords: Maximum Independent Set, Treewidth, Approximation Algorithms, Parameterized Approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.48
Kernelization for Spreading Points

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi

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

Abstract
We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of points is "close" to each other. More precisely, for a family of n points, an integer k, and a real number d > 0, we ask whether at most k points could be relocated, each point at distance at most d from its original location, such that the distance between each pair of points is at least a fixed constant, say 1. A number of approximation algorithms for variants of this problem, under different names like distant representatives, disk dispersing, or point spreading, are known in the literature. However, to the best of our knowledge, the parameterized complexity of this problem remains widely unexplored. We make the first step in this direction by providing a kernelization algorithm that, in polynomial time, produces an equivalent instance with 𝒪(d²k³) points. As a byproduct of this result, we also design a non-trivial fixed-parameter tractable (FPT) algorithm for the problem, parameterized by k and d. Finally, we complement the result about polynomial kernelization by showing a lower bound that rules out the existence of a kernel whose size is polynomial in k alone, unless NP ⊆ coNP/poly.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Kernelization for Spreading Points. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 48:1-48:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2023.48,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Saurabh, Saket and Zehavi, Meirav},
  title =	{{Kernelization for Spreading Points}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{48:1--48:16},
  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.2023.48},
  URN =		{urn:nbn:de:0030-drops-187017},
  doi =		{10.4230/LIPIcs.ESA.2023.48},
  annote =	{Keywords: parameterized algorithms, kernelization, spreading points, distant representatives, unit disk packing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.49
Lossy Kernelization for (Implicit) Hitting Set Problems

Authors: Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi

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

Abstract
We re-visit the complexity of polynomial time pre-processing (kernelization) for the d-Hitting Set problem. This is one of the most classic problems in Parameterized Complexity by itself, and, furthermore, it encompasses several other of the most well-studied problems in this field, such as Vertex Cover, Feedback Vertex Set in Tournaments (FVST) and Cluster Vertex Deletion (CVD). In fact, d-Hitting Set encompasses any deletion problem to a hereditary property that can be characterized by a finite set of forbidden induced subgraphs. With respect to bit size, the kernelization complexity of d-Hitting Set is essentially settled: there exists a kernel with 𝒪(k^d) bits (𝒪(k^d) sets and 𝒪(k^{d-1}) elements) and this it tight by the result of Dell and van Melkebeek [STOC 2010, JACM 2014]. Still, the question of whether there exists a kernel for d-Hitting Set with fewer elements has remained one of the most major open problems in Kernelization. In this paper, we first show that if we allow the kernelization to be lossy with a qualitatively better loss than the best possible approximation ratio of polynomial time approximation algorithms, then one can obtain kernels where the number of elements is linear for every fixed d. Further, based on this, we present our main result: we show that there exist approximate Turing kernelizations for d-Hitting Set that even beat the established bit-size lower bounds for exact kernelizations - in fact, we use a constant number of oracle calls, each with "near linear" (𝒪(k^{1+ε})) bit size, that is, almost the best one could hope for. Lastly, for two special cases of implicit 3-Hitting set, namely, FVST and CVD, we obtain the "best of both worlds" type of results - (1+ε)-approximate kernelizations with a linear number of vertices. In terms of size, this substantially improves the exact kernels of Fomin et al. [SODA 2018, TALG 2019], with simpler arguments.
Cite as

Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi. Lossy Kernelization for (Implicit) Hitting Set Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 49:1-49:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2023.49,
  author =	{Fomin, Fedor V. and Le, Tien-Nam and Lokshtanov, Daniel and Saurabh, Saket and Thomass\'{e}, St\'{e}phan and Zehavi, Meirav},
  title =	{{Lossy Kernelization for (Implicit) Hitting Set Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{49:1--49:14},
  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.2023.49},
  URN =		{urn:nbn:de:0030-drops-187020},
  doi =		{10.4230/LIPIcs.ESA.2023.49},
  annote =	{Keywords: Hitting Set, Lossy Kernelization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.46
FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, and Tomohiro Koana

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

Abstract
We study the α-Fixed Cardinality Graph Partitioning (α-FCGP) problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph G, two numbers k,p and 0 ≤ α ≤ 1, the question is whether there is a set S ⊆ V of size k with a specified coverage function cov_α(S) at least p (or at most p for the minimization version). The coverage function cov_α(⋅) counts edges with exactly one endpoint in S with weight α and edges with both endpoints in S with weight 1 - α. α-FCGP generalizes a number of fundamental graph problems such as Densest k-Subgraph, Max k-Vertex Cover, and Max (k,n-k)-Cut. A natural question in the study of α-FCGP is whether the algorithmic results known for its special cases, like Max k-Vertex Cover, could be extended to more general settings. One of the simple but powerful methods for obtaining parameterized approximation [Manurangsi, SOSA 2019] and subexponential algorithms [Fomin et al. IPL 2011] for Max k-Vertex Cover is based on the greedy vertex degree orderings. The main insight of our work is that the idea of greed vertex degree ordering could be used to design fixed-parameter approximation schemes (FPT-AS) for α > 0 and the subexponential-time algorithms for the problem on apex-minor free graphs for maximization with α > 1/3 and minimization with α < 1/3.
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, and Tomohiro Koana. FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 46:1-46:8, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.MFCS.2023.46,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Koana, Tomohiro},
  title =	{{FPT Approximation and Subexponential Algorithms for Covering Few or Many Edges}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{46:1--46:8},
  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.2023.46},
  URN =		{urn:nbn:de:0030-drops-185806},
  doi =		{10.4230/LIPIcs.MFCS.2023.46},
  annote =	{Keywords: Partial Vertex Cover, Approximation Algorithms, Max Cut}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.3
Partitioning the Bags of a Tree Decomposition into Cliques

Authors: Thomas Bläsius, Maximilian Katzmann, and Marcus Wilhelm

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With this paper, we take a first step towards computing clique-partitioned tree decompositions. Our focus lies on the subproblem of computing clique partitions, i.e., for each bag of a given tree decomposition, we compute an optimal partition of the induced subgraph into cliques. The goal here is to minimize the product of the clique sizes (plus 1). We show that this problem is NP-hard. We also describe four heuristic approaches as well as an exact branch-and-bound algorithm. Our evaluation shows that the branch-and-bound solver is sufficiently efficient to serve as a good baseline. Moreover, our heuristics yield solutions close to the optimum. As a bonus, our algorithms allow us to compute first upper bounds for the clique-partitioned treewidth of real-world networks. A comparison to traditional treewidth indicates that clique-partitioned treewidth is a promising parameter for graphs with high clustering.
Cite as

Thomas Bläsius, Maximilian Katzmann, and Marcus Wilhelm. Partitioning the Bags of a Tree Decomposition into Cliques. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 3:1-3:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blasius_et_al:LIPIcs.SEA.2023.3,
  author =	{Bl\"{a}sius, Thomas and Katzmann, Maximilian and Wilhelm, Marcus},
  title =	{{Partitioning the Bags of a Tree Decomposition into Cliques}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.3},
  URN =		{urn:nbn:de:0030-drops-183533},
  doi =		{10.4230/LIPIcs.SEA.2023.3},
  annote =	{Keywords: treewidth, weighted treewidth, algorithm engineering, cliques, clustering, complex networks}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.10
Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover

Authors: Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ⊆ V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.
Cite as

Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 10:1-10:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{angrick_et_al:LIPIcs.SEA.2023.10,
  author =	{Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Ki{\ss}ig, Otto and Schmidt, Jonas and Wendt, Leo},
  title =	{{Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.10},
  URN =		{urn:nbn:de:0030-drops-183602},
  doi =		{10.4230/LIPIcs.SEA.2023.10},
  annote =	{Keywords: directed feedback vertex set, vertex cover, reduction rules}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.14
A Graph-Theoretic Formulation of Exploratory Blockmodeling

Authors: Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G' with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G' directly give the blocks and block interactions of the computed blockmodel. We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ≥ 4.
Cite as

Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. A Graph-Theoretic Formulation of Exploratory Blockmodeling. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 14:1-14:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bille_et_al:LIPIcs.SEA.2023.14,
  author =	{Bille, Alexander and Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Graph-Theoretic Formulation of Exploratory Blockmodeling}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.14},
  URN =		{urn:nbn:de:0030-drops-183648},
  doi =		{10.4230/LIPIcs.SEA.2023.14},
  annote =	{Keywords: Clustering, Exact Algorithms, ILP-Formulation, Branch-and-Bound, Social Networks}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.60
Approximating Long Cycle Above Dirac’s Guarantee

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

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

Abstract
Parameterization above (or below) a guarantee is a successful concept in parameterized algorithms. The idea is that many computational problems admit "natural" guarantees bringing to algorithmic questions whether a better solution (above the guarantee) could be obtained efficiently. For example, for every boolean CNF formula on m clauses, there is an assignment that satisfies at least m/2 clauses. How difficult is it to decide whether there is an assignment satisfying more than m/2 + k clauses? Or, if an n-vertex graph has a perfect matching, then its vertex cover is at least n/2. Is there a vertex cover of size at least n/2 + k for some k ≥ 1 and how difficult is it to find such a vertex cover? The above guarantee paradigm has led to several exciting discoveries in the areas of parameterized algorithms and kernelization. We argue that this paradigm could bring forth fresh perspectives on well-studied problems in approximation algorithms. Our example is the longest cycle problem. One of the oldest results in extremal combinatorics is the celebrated Dirac’s theorem from 1952. Dirac’s theorem provides the following guarantee on the length of the longest cycle: for every 2-connected n-vertex graph G with minimum degree δ(G) ≤ n/2, the length of the longest cycle L is at least 2δ(G). Thus the "essential" part of finding the longest cycle is in approximating the "offset" k = L - 2δ(G). The main result of this paper is the above-guarantee approximation theorem for k. Informally, the theorem says that approximating the offset k is not harder than approximating the total length L of a cycle. In other words, for any (reasonably well-behaved) function f, a polynomial time algorithm constructing a cycle of length f(L) in an undirected graph with a cycle of length L, yields a polynomial time algorithm constructing a cycle of length 2δ(G)+Ω(f(k)).
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Approximating Long Cycle Above Dirac’s Guarantee. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 60:1-60:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ICALP.2023.60,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Approximating Long Cycle Above Dirac’s Guarantee}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{60:1--60:18},
  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.2023.60},
  URN =		{urn:nbn:de:0030-drops-181128},
  doi =		{10.4230/LIPIcs.ICALP.2023.60},
  annote =	{Keywords: Longest path, longest cycle, approximation algorithms, above guarantee parameterization, minimum degree, Dirac theorem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.61
Compound Logics for Modification Problems

Authors: Fedor V. Fomin, Petr A. Golovach, Ignasi Sau, Giannos Stamoulis, and Dimitrios M. Thilikos

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

Abstract
We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of sentences, expressing graph modification: the modulator sentence, defining some property of the modified part of the graph, and the target sentence, defining some property of the resulting graph. In our framework, modulator sentences are in counting monadic second-order logic (CMSOL) and have models of bounded treewidth, while target sentences express first-order logic (FOL) properties along with minor-exclusion. Our logic captures problems that are not definable in first-order logic and, moreover, may have instances of unbounded treewidth. Also, it permits the modeling of wide families of problems involving vertex/edge removals, alternative modulator measures (such as elimination distance or G-treewidth), multistage modifications, and various cut problems. Our main result is that, for this compound logic, model-checking can be done in quadratic time. All derived algorithms are constructive and this, as a byproduct, extends the constructibility horizon of the algorithmic applications of the Graph Minors theorem of Robertson and Seymour. The proposed logic can be seen as a general framework to capitalize on the potential of the irrelevant vertex technique. It gives a way to deal with problem instances of unbounded treewidth, for which Courcelle’s theorem does not apply.
Cite as

Fedor V. Fomin, Petr A. Golovach, Ignasi Sau, Giannos Stamoulis, and Dimitrios M. Thilikos. Compound Logics for Modification Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 61:1-61:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fomin_et_al:LIPIcs.ICALP.2023.61,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sau, Ignasi and Stamoulis, Giannos and Thilikos, Dimitrios M.},
  title =	{{Compound Logics for Modification Problems}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{61:1--61:21},
  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.2023.61},
  URN =		{urn:nbn:de:0030-drops-181137},
  doi =		{10.4230/LIPIcs.ICALP.2023.61},
  annote =	{Keywords: Algorithmic meta-theorems, Graph modification problems, Model-checking, Graph minors, First-order logic, Monadic second-order logic, Flat Wall theorem, Irrelevant vertex technique}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.10
Coresets for Clustering in Geometric Intersection Graphs

Authors: Sayan Bandyapadhyay, Fedor V. Fomin, and Tanmay Inamdar

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
Designing coresets - small-space sketches of the data preserving cost of the solutions within (1± ε)-approximate factor - is an important research direction in the study of center-based k-clustering problems, such as k-means or k-median. Feldman and Langberg [STOC'11] have shown that for k-clustering of n points in general metrics, it is possible to obtain coresets whose size depends logarithmically in n. Moreover, such a dependency in n is inevitable in general metrics. A significant amount of recent work in the area is devoted to obtaining coresests whose sizes are independent of n for special metrics, like d-dimensional Euclidean space [Huang, Vishnoi, STOC'20], doubling metrics [Huang, Jiang, Li, Wu, FOCS'18], metrics of graphs of bounded treewidth [Baker, Braverman, Huang, Jiang, Krauthgamer, Wu, ICML’20], or graphs excluding a fixed minor [Braverman, Jiang, Krauthgamer, Wu, SODA’21]. In this paper, we provide the first constructions of coresets whose size does not depend on n for k-clustering in the metrics induced by geometric intersection graphs. For example, we obtain (k log²k)/ε^𝒪(1) size coresets for k-clustering in Euclidean-weighted unit-disk graphs (UDGs) and unit-square graphs (USGs). These constructions follow from a general theorem that identifies two canonical properties of a graph metric sufficient for obtaining coresets whose size is independent of n. The proof of our theorem builds on the recent work of Cohen-Addad, Saulpic, and Schwiegelshohn [STOC '21], which ensures small-sized coresets conditioned on the existence of an interesting set of centers, called centroid set. The main technical contribution of our work is the proof of the existence of such a small-sized centroid set for graphs that satisfy the two canonical properties. Loosely speaking, the metrics of geometric intersection graphs are "similar" to the Euclidean metrics for points that are close, and to the shortest path metrics of planar graphs for points that are far apart. The main technical challenge in constructing centroid sets of small sizes is in combining these two very different metrics. The new coreset construction helps to design the first (1+ε)-approximation for center-based clustering problems in UDGs and USGs, that is fixed-parameter tractable in k and ε (FPT-AS).
Cite as

Sayan Bandyapadhyay, Fedor V. Fomin, and Tanmay Inamdar. Coresets for Clustering in Geometric Intersection Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 10:1-10:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.SoCG.2023.10,
  author =	{Bandyapadhyay, Sayan and Fomin, Fedor V. and Inamdar, Tanmay},
  title =	{{Coresets for Clustering in Geometric Intersection Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.10},
  URN =		{urn:nbn:de:0030-drops-178605},
  doi =		{10.4230/LIPIcs.SoCG.2023.10},
  annote =	{Keywords: k-median, k-means, clustering, coresets, geometric graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.4
FPT Approximation for Fair Minimum-Load Clustering

Authors: Sayan Bandyapadhyay, Fedor V. Fomin, Petr A. Golovach, Nidhi Purohit, and Kirill Simonov

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
In this paper, we consider the Minimum-Load k-Clustering/Facility Location (MLkC) problem where we are given a set P of n points in a metric space that we have to cluster and an integer k > 0 that denotes the number of clusters. Additionally, we are given a set F of cluster centers in the same metric space. The goal is to select a set C ⊆ F of k centers and assign each point in P to a center in C, such that the maximum load over all centers is minimized. Here the load of a center is the sum of the distances between it and the points assigned to it. Although clustering/facility location problems have rich literature, the minimum-load objective has not been studied substantially, and hence MLkC has remained a poorly understood problem. More interestingly, the problem is notoriously hard even in some special cases including the one in line metrics as shown by Ahmadian et al. [APPROX 2014, ACM Trans. Algorithms 2018]. They also show APX-hardness of the problem in the plane. On the other hand, the best-known approximation factor for MLkC is O(k), even in the plane. In this work, we study a fair version of MLkC inspired by the work of Chierichetti et al. [NeurIPS, 2017]. Here the input points are partitioned into 𝓁 protected groups, and only clusters that proportionally represent each group are allowed. MLkC is the special case with 𝓁 = 1. For the fair version, we are able to obtain a randomized 3-approximation algorithm in f(k,𝓁)⋅ n^O(1) time. Also, our scheme leads to an improved (1 + ε)-approximation in the case of Euclidean norm with the same running time (depending also linearly on the dimension d). Our results imply the same approximations for MLkC with running time f(k)⋅ n^O(1), achieving the first constant-factor FPT approximations for this problem in general and Euclidean metric spaces.
Cite as

Sayan Bandyapadhyay, Fedor V. Fomin, Petr A. Golovach, Nidhi Purohit, and Kirill Simonov. FPT Approximation for Fair Minimum-Load Clustering. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 4:1-4:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.IPEC.2022.4,
  author =	{Bandyapadhyay, Sayan and Fomin, Fedor V. and Golovach, Petr A. and Purohit, Nidhi and Simonov, Kirill},
  title =	{{FPT Approximation for Fair Minimum-Load Clustering}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.4},
  URN =		{urn:nbn:de:0030-drops-173600},
  doi =		{10.4230/LIPIcs.IPEC.2022.4},
  annote =	{Keywords: fair clustering, load balancing, parameterized approximation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.13
Exact Exponential Algorithms for Clustering Problems

Authors: Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Nidhi Purohit, and Saket Saurabh

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
In this paper we initiate a systematic study of exact algorithms for some of the well known clustering problems, namely k-MEDIAN and k-MEANS. In k-MEDIAN, the input consists of a set X of n points belonging to a metric space, and the task is to select a subset C ⊆ X of k points as centers, such that the sum of the distances of every point to its nearest center is minimized. In k-MEANS, the objective is to minimize the sum of squares of the distances instead. It is easy to design an algorithm running in time max_{k ≤ n} {n choose k} n^𝒪(1) = 𝒪^*(2ⁿ) (here, 𝒪^*(⋅) notation hides polynomial factors in n). In this paper we design first non-trivial exact algorithms for these problems. In particular, we obtain an 𝒪^*((1.89)ⁿ) time exact algorithm for k-MEDIAN that works for any value of k. Our algorithm is quite general in that it does not use any properties of the underlying (metric) space - it does not even require the distances to satisfy the triangle inequality. In particular, the same algorithm also works for k-Means. We complement this result by showing that the running time of our algorithm is asymptotically optimal, up to the base of the exponent. That is, unless the Exponential Time Hypothesis fails, there is no algorithm for these problems running in time 2^o(n)⋅n^𝒪(1). Finally, we consider the "facility location" or "supplier" versions of these clustering problems, where, in addition to the set X we are additionally given a set of m candidate centers (or facilities) F, and objective is to find a subset of k centers from F. The goal is still to minimize the k-Median/k-Means/k-Center objective. For these versions we give a 𝒪(2ⁿ (mn)^𝒪(1)) time algorithms using subset convolution. We complement this result by showing that, under the Set Cover Conjecture, the "supplier" versions of these problems do not admit an exact algorithm running in time 2^{(1-ε) n} (mn)^𝒪(1).
Cite as

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Nidhi Purohit, and Saket Saurabh. Exact Exponential Algorithms for Clustering Problems. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 13:1-13:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fomin_et_al:LIPIcs.IPEC.2022.13,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Inamdar, Tanmay and Purohit, Nidhi and Saurabh, Saket},
  title =	{{Exact Exponential Algorithms for Clustering Problems}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.13},
  URN =		{urn:nbn:de:0030-drops-173691},
  doi =		{10.4230/LIPIcs.IPEC.2022.13},
  annote =	{Keywords: clustering, k-median, k-means, exact algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.55
Longest Cycle Above Erdős-Gallai Bound

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

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

Abstract
In 1959, Erdős and Gallai proved that every graph G with average vertex degree ad(G) ≥ 2 contains a cycle of length at least ad(G). We provide an algorithm that for k ≥ 0 in time 2^𝒪(k)⋅n^𝒪(1) decides whether a 2-connected n-vertex graph G contains a cycle of length at least ad(G)+k. This resolves an open problem explicitly mentioned in several papers. The main ingredients of our algorithm are new graph-theoretical results interesting on their own.
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Longest Cycle Above Erdős-Gallai Bound. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 55:1-55:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2022.55,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Longest Cycle Above Erd\H{o}s-Gallai Bound}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{55:1--55:15},
  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.2022.55},
  URN =		{urn:nbn:de:0030-drops-169935},
  doi =		{10.4230/LIPIcs.ESA.2022.55},
  annote =	{Keywords: Longest path, longest cycle, fixed-parameter tractability, above guarantee parameterization, average degree, Erd\H{o}s and Gallai theorem}
}
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