20 Search Results for "Wahlström, Magnus"

Volume

LIPIcs, Volume 285

18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

IPEC 2023, September 6-8, 2023, Amsterdam, The Netherlands

Editors: Neeldhara Misra and Magnus Wahlström

Document
DOI: 10.4230/LIPIcs.ESA.2024.93
Parameterized Complexity of MinCSP over the Point Algebra

Authors: George Osipov, Marcin Pilipczuk, and Magnus Wahlström

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

Abstract
The input in the Minimum-Cost Constraint Satisfaction Problem (MinCSP) over the Point Algebra contains a set of variables, a collection of constraints of the form x < y, x = y, x ≤ y and x ≠ y, and a budget k. The goal is to check whether it is possible to assign rational values to the variables while breaking constraints of total cost at most k. This problem generalizes several prominent graph separation and transversal problems: - MinCSP({<}) is equivalent to Directed Feedback Arc Set, - MinCSP({< , ≤}) is equivalent to Directed Subset Feedback Arc Set, - MinCSP({= ,≠}) is equivalent to Edge Multicut, and - MinCSP({≤ ,≠}) is equivalent to Directed Symmetric Multicut. Apart from trivial cases, MinCSP({Γ}) for Γ ⊆ {< , = , ≤ ,≠} is NP-hard even to approximate within any constant factor under the Unique Games Conjecture. Hence, we study parameterized complexity of this problem under a natural parameterization by the solution cost k. We obtain a complete classification: if Γ ⊆ {< , = , ≤ ,≠} contains both ≤ and ≠, then MinCSP({Γ}) is W[1]-hard, otherwise it is fixed-parameter tractable. For the positive cases, we solve MinCSP({< , = ,≠}), generalizing the FPT results for Directed Feedback Arc Set and Edge Multicut as well as their weighted versions. Our algorithm works by reducing the problem into a Boolean MinCSP, which is in turn solved by flow augmentation. For the lower bounds, we prove that Directed Symmetric Multicut is W[1]-hard, solving an open problem.
Cite as

George Osipov, Marcin Pilipczuk, and Magnus Wahlström. Parameterized Complexity of MinCSP over the Point Algebra. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 93:1-93:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{osipov_et_al:LIPIcs.ESA.2024.93,
  author =	{Osipov, George and Pilipczuk, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Complexity of MinCSP over the Point Algebra}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{93:1--93:15},
  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.2024.93},
  URN =		{urn:nbn:de:0030-drops-211640},
  doi =		{10.4230/LIPIcs.ESA.2024.93},
  annote =	{Keywords: parameterized complexity, constraint satisfaction, point algebra, multicut, feedback arc set}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.IPEC.2023
LIPIcs, Volume 285, IPEC 2023, Complete Volume

Authors: Neeldhara Misra and Magnus Wahlström

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
LIPIcs, Volume 285, IPEC 2023, Complete Volume
Cite as

18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 1-644, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{misra_et_al:LIPIcs.IPEC.2023,
  title =	{{LIPIcs, Volume 285, IPEC 2023, Complete Volume}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{1--644},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023},
  URN =		{urn:nbn:de:0030-drops-194183},
  doi =		{10.4230/LIPIcs.IPEC.2023},
  annote =	{Keywords: LIPIcs, Volume 285, IPEC 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.IPEC.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Neeldhara Misra and Magnus Wahlström

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{misra_et_al:LIPIcs.IPEC.2023.0,
  author =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.0},
  URN =		{urn:nbn:de:0030-drops-194191},
  doi =		{10.4230/LIPIcs.IPEC.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.86
Parameterized Complexity of Equality MinCSP

Authors: George Osipov and Magnus Wahlström

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

Abstract
We study the parameterized complexity of MinCSP for so-called equality languages, i.e., for finite languages over an infinite domain such as ℕ, where the relations are defined via first-order formulas whose only predicate is =. This is an important class of languages that forms the starting point of all study of infinite-domain CSPs under the commonly used approach pioneered by Bodirsky, i.e., languages defined as reducts of finitely bounded homogeneous structures. Moreover, MinCSP over equality languages forms a natural class of optimisation problems in its own right, covering such problems as Edge Multicut, Steiner Multicut and (under singleton expansion) Edge Multiway Cut. We classify MinCSP(Γ) for every finite equality language Γ, under the natural parameter, as either FPT, W[1]-hard but admitting a constant-factor FPT-approximation, or not admitting a constant-factor FPT-approximation unless FPT=W[2]. In particular, we describe an FPT case that slightly generalises Multicut, and show a constant-factor FPT-approximation for Disjunctive Multicut, the generalisation of Multicut where the "cut requests" come as disjunctions over O(1) individual cut requests s_i ≠ t_i. We also consider singleton expansions of equality languages, enriching an equality language with the capability for assignment constraints (x = i) for either a finite or infinitely many constants i, and fully characterize the complexity of the resulting MinCSP.
Cite as

George Osipov and Magnus Wahlström. Parameterized Complexity of Equality MinCSP. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 86:1-86:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{osipov_et_al:LIPIcs.ESA.2023.86,
  author =	{Osipov, George and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Complexity of Equality MinCSP}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{86:1--86:17},
  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.2023.86},
  URN =		{urn:nbn:de:0030-drops-187393},
  doi =		{10.4230/LIPIcs.ESA.2023.86},
  annote =	{Keywords: parameterized complexity, constraint satisfaction, parameterized approximation}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.11
On the Parameterized Complexity of Symmetric Directed Multicut

Authors: Eduard Eiben, Clément Rambaud, and Magnus Wahlström

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

Abstract
We study the problem Symmetric Directed Multicut from a parameterized complexity perspective. In this problem, the input is a digraph D, a set of cut requests C = {(s₁,t₁),…,(s_l,t_l)} and an integer k, and the task is to find a set X ⊆ V(D) of size at most k such that for every 1 ≤ i ≤ l, X intersects either all (s_i,t_i)-paths or all (t_i,s_i)-paths. Equivalently, every strongly connected component of D-X contains at most one vertex out of s_i and t_i for every i. This problem is previously known from research in approximation algorithms, where it is known to have an O(log k log log k)-approximation. We note that the problem, parameterized by k, directly generalizes multiple interesting FPT problems such as (Undirected) Vertex Multicut and Directed Subset Feedback Vertex Set. We are not able to settle the existence of an FPT algorithm parameterized purely by k, but we give three partial results: An FPT algorithm parameterized by k+l; an FPT-time 2-approximation parameterized by k; and an FPT algorithm parameterized by k for the special case that the cut requests form a clique, Symmetric Directed Multiway Cut. The existence of an FPT algorithm parameterized purely by k remains an intriguing open possibility.
Cite as

Eduard Eiben, Clément Rambaud, and Magnus Wahlström. On the Parameterized Complexity of Symmetric Directed Multicut. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{eiben_et_al:LIPIcs.IPEC.2022.11,
  author =	{Eiben, Eduard and Rambaud, Cl\'{e}ment and Wahlstr\"{o}m, Magnus},
  title =	{{On the Parameterized Complexity of Symmetric Directed Multicut}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{11:1--11:17},
  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.2022.11},
  URN =		{urn:nbn:de:0030-drops-173679},
  doi =		{10.4230/LIPIcs.IPEC.2022.11},
  annote =	{Keywords: Parameterized complexity, directed graphs, graph separation problems}
}
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
DOI: 10.4230/LIPIcs.ESA.2021.52
Near-Linear-Time, Optimal Vertex Cut Sparsifiers in Directed Acyclic Graphs

Authors: Zhiyang He, Jason Li, and Magnus Wahlström

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Let G be a graph and S, T ⊆ V(G) be (possibly overlapping) sets of terminals, |S| = |T| = k. We are interested in computing a vertex sparsifier for terminal cuts in G, i.e., a graph H on a smallest possible number of vertices, where S ∪ T ⊆ V(H) and such that for every A ⊆ S and B ⊆ T the size of a minimum (A,B)-vertex cut is the same in G as in H. We assume that our graphs are unweighted and that terminals may be part of the min-cut. In previous work, Kratsch and Wahlström (FOCS 2012/JACM 2020) used connections to matroid theory to show that a vertex sparsifier H with O(k³) vertices can be computed in randomized polynomial time, even for arbitrary digraphs G. However, since then, no improvements on the size O(k³) have been shown. In this paper, we draw inspiration from the renowned Bollobás’s Two-Families Theorem in extremal combinatorics and introduce the use of total orderings into Kratsch and Wahlström’s methods. This new perspective allows us to construct a sparsifier H of Θ(k²) vertices for the case that G is a DAG. We also show how to compute H in time near-linear in the size of G, improving on the previous O(n^{ω+1}). Furthermore, H recovers the closest min-cut in G for every partition (A,B), which was not previously known. Finally, we show that a sparsifier of size Ω(k²) is required, both for DAGs and for undirected edge cuts.
Cite as

Zhiyang He, Jason Li, and Magnus Wahlström. Near-Linear-Time, Optimal Vertex Cut Sparsifiers in Directed Acyclic Graphs. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{he_et_al:LIPIcs.ESA.2021.52,
  author =	{He, Zhiyang and Li, Jason and Wahlstr\"{o}m, Magnus},
  title =	{{Near-Linear-Time, Optimal Vertex Cut Sparsifiers in Directed Acyclic Graphs}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{52:1--52:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.52},
  URN =		{urn:nbn:de:0030-drops-146331},
  doi =		{10.4230/LIPIcs.ESA.2021.52},
  annote =	{Keywords: graph theory, vertex sparsifier, representative family, matroid}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.2
Component Order Connectivity in Directed Graphs

Authors: Jørgen Bang-Jensen, Eduard Eiben, Gregory Gutin, Magnus Wahlström, and Anders Yeo

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

Abstract
A directed graph D is semicomplete if for every pair x,y of vertices of D, there is at least one arc between x and y. Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph D = (V,A) and a pair of natural numbers k and 𝓁, we are to decide whether there is a subset X of V of size k such that the largest strong connectivity component in D-X has at most 𝓁 vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for 𝓁 = 1. We study parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters: k, 𝓁, 𝓁+k and n-𝓁. In particular, we prove that DCOC with parameter k on semicomplete digraphs can be solved in time O^*(2^(16k)) but not in time O^*(2^o(k)) unless the Exponential Time Hypothesis (ETH) fails. The upper bound O^*(2^(16k)) implies the upper bound O^*(2^(16(n-𝓁))) for the parameter n-𝓁. We complement the latter by showing that there is no algorithm of time complexity O^*(2^o(n-𝓁)) unless ETH fails. Finally, we improve (in dependency on 𝓁) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter 𝓁+k on general digraphs from O^*(2^O(k𝓁 log (k𝓁))) to O^*(2^O(klog (k𝓁))). Note that Drange, Dregi and van 't Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time O^*(2^o(klog 𝓁)) unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity O^*(2^o(klog k)).
Cite as

Jørgen Bang-Jensen, Eduard Eiben, Gregory Gutin, Magnus Wahlström, and Anders Yeo. Component Order Connectivity in Directed Graphs. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bangjensen_et_al:LIPIcs.IPEC.2020.2,
  author =	{Bang-Jensen, J{\o}rgen and Eiben, Eduard and Gutin, Gregory and Wahlstr\"{o}m, Magnus and Yeo, Anders},
  title =	{{Component Order Connectivity in Directed Graphs}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{2:1--2:16},
  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.2020.2},
  URN =		{urn:nbn:de:0030-drops-133058},
  doi =		{10.4230/LIPIcs.IPEC.2020.2},
  annote =	{Keywords: Parameterized Algorithms, component order connectivity, directed graphs, semicomplete digraphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.66
Many Visits TSP Revisited

Authors: Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We study the Many Visits TSP problem, where given a number k(v) for each of n cities and pairwise (possibly asymmetric) integer distances, one has to find an optimal tour that visits each city v exactly k(v) times. The currently fastest algorithm is due to Berger, Kozma, Mnich and Vincze [SODA 2019, TALG 2020] and runs in time and space O*(5ⁿ). They also show a polynomial space algorithm running in time O(16^{n+o(n)}). In this work, we show three main results: - A randomized polynomial space algorithm in time O*(2^n D), where D is the maximum distance between two cities. By using standard methods, this results in a (1+ε)-approximation in time O*(2ⁿε^{-1}). Improving the constant 2 in these results would be a major breakthrough, as it would result in improving the O*(2ⁿ)-time algorithm for Directed Hamiltonian Cycle, which is a 50 years old open problem. - A tight analysis of Berger et al.’s exponential space algorithm, resulting in an O*(4ⁿ) running time bound. - A new polynomial space algorithm, running in time O(7.88ⁿ).
Cite as

Łukasz Kowalik, Shaohua Li, Wojciech Nadara, Marcin Smulewicz, and Magnus Wahlström. Many Visits TSP Revisited. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kowalik_et_al:LIPIcs.ESA.2020.66,
  author =	{Kowalik, {\L}ukasz and Li, Shaohua and Nadara, Wojciech and Smulewicz, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Many Visits TSP Revisited}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.66},
  URN =		{urn:nbn:de:0030-drops-129329},
  doi =		{10.4230/LIPIcs.ESA.2020.66},
  annote =	{Keywords: many visits traveling salesman problem, exponential algorithm}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.11
Solving Packing Problems with Few Small Items Using Rainbow Matchings

Authors: Max Bannach, Sebastian Berndt, Marten Maack, Matthias Mnich, Alexandra Lassota, Malin Rau, and Malte Skambath

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation algorithms, but their parameterized complexity has only been investigated barely. For problem instances containing no "small" items, classical matching algorithms yield optimal solutions in polynomial time. In this paper we approach them by their distance from triviality, measuring the problem complexity by the number k of small items. Our main results are fixed-parameter algorithms for vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by k. The algorithms are randomized with one-sided error and run in time 4^k⋅ k!⋅ n^{O(1)}. To achieve this, we introduce a colored matching problem to which we reduce all these packing problems. The colored matching problem is natural in itself and we expect it to be useful for other applications. We also present a deterministic fixed-parameter algorithm for Bin Covering with run time O((k!)² ⋅ k ⋅ 2^k ⋅ n log(n)).
Cite as

Max Bannach, Sebastian Berndt, Marten Maack, Matthias Mnich, Alexandra Lassota, Malin Rau, and Malte Skambath. Solving Packing Problems with Few Small Items Using Rainbow Matchings. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bannach_et_al:LIPIcs.MFCS.2020.11,
  author =	{Bannach, Max and Berndt, Sebastian and Maack, Marten and Mnich, Matthias and Lassota, Alexandra and Rau, Malin and Skambath, Malte},
  title =	{{Solving Packing Problems with Few Small Items Using Rainbow Matchings}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.11},
  URN =		{urn:nbn:de:0030-drops-126816},
  doi =		{10.4230/LIPIcs.MFCS.2020.11},
  annote =	{Keywords: Bin Packing, Knapsack, matching, fixed-parameter tractable}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.101
On Quasipolynomial Multicut-Mimicking Networks and Kernelization of Multiway Cut Problems

Authors: Magnus Wahlström

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We show the existence of an exact mimicking network of k^O(log k) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals. Furthermore, if Small Set Expansion has an approximation algorithm with a ratio slightly better than Θ(log n), then a mimicking network of quasipolynomial size can be computed in polynomial time. As a consequence of the latter, several problems would have quasipolynomial kernels, including Edge Multiway Cut, Group Feedback Edge Set for an arbitrary group, 0-Extension for integer-weighted metrics, and Edge Multicut parameterized by the solution and the number of cut requests. The result works via a combination of the matroid-based irrelevant edge approach used in the kernel for s-Multiway Cut with a recursive decomposition and sparsification of the graph along sparse cuts. The main technical contribution is a matroid-based marking procedure that we can show will mark all non-irrelevant edges, assuming that the graph is sufficiently densely connected. The only part of the result that is not currently constructive and polynomial-time computable is the detection of such sparse cuts. This is the first progress on the kernelization of Multiway Cut problems since the kernel for s-Multiway Cut for constant value of s (Kratsch and Wahlström, FOCS 2012).
Cite as

Magnus Wahlström. On Quasipolynomial Multicut-Mimicking Networks and Kernelization of Multiway Cut Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 101:1-101:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wahlstrom:LIPIcs.ICALP.2020.101,
  author =	{Wahlstr\"{o}m, Magnus},
  title =	{{On Quasipolynomial Multicut-Mimicking Networks and Kernelization of Multiway Cut Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{101:1--101:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.101},
  URN =		{urn:nbn:de:0030-drops-125082},
  doi =		{10.4230/LIPIcs.ICALP.2020.101},
  annote =	{Keywords: Multiway Cut, Kernelization, Small Set Expansion, Mimicking Networks}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.19
Parameterized Pre-Coloring Extension and List Coloring Problems

Authors: Gregory Gutin, Diptapriyo Majumdar, Sebastian Ordyniak, and Magnus Wahlström

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by k: (1) Given a graph G, a clique modulator D (a clique modulator is a set of vertices, whose removal results in a clique) of size k for G, and a list L(v) of colors for every v ∈ V(G), decide whether G has a proper list coloring; (2) Given a graph G, a clique modulator D of size k for G, and a pre-coloring λ_P: X → Q for X ⊆ V(G), decide whether λ_P can be extended to a proper coloring of G using only colors from Q. For Problem 1 we design an O*(2^k)-time randomized algorithm and for Problem 2 we obtain a kernel with at most 3k vertices. Banik et al. (IWOCA 2019) proved the following problem is fixed-parameter tractable and asked whether it admits a polynomial kernel: Given a graph G, an integer k, and a list L(v) of exactly n-k colors for every v ∈ V(G), decide whether there is a proper list coloring for G. We obtain a kernel with O(k²) vertices and colors and a compression to a variation of the problem with O(k) vertices and O(k²) colors.
Cite as

Gregory Gutin, Diptapriyo Majumdar, Sebastian Ordyniak, and Magnus Wahlström. Parameterized Pre-Coloring Extension and List Coloring Problems. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gutin_et_al:LIPIcs.STACS.2020.19,
  author =	{Gutin, Gregory and Majumdar, Diptapriyo and Ordyniak, Sebastian and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Pre-Coloring Extension and List Coloring Problems}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.19},
  URN =		{urn:nbn:de:0030-drops-118801},
  doi =		{10.4230/LIPIcs.STACS.2020.19},
  annote =	{Keywords: Parameterized Algorithms, W-hardness, Kernelization, Graph Coloring, List Coloring}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.18
Multi-Budgeted Directed Cuts

Authors: Stefan Kratsch, Shaohua Li, Dániel Marx, Marcin Pilipczuk, and Magnus Wahlström

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract
In this paper, we study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign colors 1,2,...,l to some edges and give separate budgets k_1,k_2,...,k_l for colors 1,2,...,l. For every color i in {1,...,l}, let E_i be the set of edges of color i. The solution C for the multi-budgeted variant of a graph separation problem not only needs to satisfy the usual separation requirements (i.e., be a cut, a skew multicut, or a directed feedback arc set, respectively), but also needs to satisfy that |C cap E_i| <= k_i for every i in {1,...,l}. Contrary to the classic minimum cut problem, the multi-budgeted variant turns out to be NP-hard even for l = 2. We propose FPT algorithms parameterized by k=k_1 +...+ k_l for all three problems. To this end, we develop a branching procedure for the multi-budgeted minimum cut problem that measures the progress of the algorithm not by reducing k as usual, by but elevating the capacity of some edges and thus increasing the size of maximum source-to-sink flow. Using the fact that a similar strategy is used to enumerate all important separators of a given size, we merge this process with the flow-guided branching and show an FPT bound on the number of (appropriately defined) important multi-budgeted separators. This allows us to extend our algorithm to the Skew Multicut and Directed Feedback Arc Set problems. Furthermore, we show connections of the multi-budgeted variants with weighted variants of the directed cut problems and the Chain l-SAT problem, whose parameterized complexity remains an open problem. We show that these problems admit a bounded-in-parameter number of "maximally pushed" solutions (in a similar spirit as important separators are maximally pushed), giving somewhat weak evidence towards their tractability.
Cite as

Stefan Kratsch, Shaohua Li, Dániel Marx, Marcin Pilipczuk, and Magnus Wahlström. Multi-Budgeted Directed Cuts. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kratsch_et_al:LIPIcs.IPEC.2018.18,
  author =	{Kratsch, Stefan and Li, Shaohua and Marx, D\'{a}niel and Pilipczuk, Marcin and Wahlstr\"{o}m, Magnus},
  title =	{{Multi-Budgeted Directed Cuts}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.18},
  URN =		{urn:nbn:de:0030-drops-102194},
  doi =		{10.4230/LIPIcs.IPEC.2018.18},
  annote =	{Keywords: important separators, multi-budgeted cuts, Directed Feedback Vertex Set, fixed-parameter tractability, minimum cut}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.94
Parameterized Algorithms for Zero Extension and Metric Labelling Problems

Authors: Felix Reidl and Magnus Wahlström

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We consider the problems Zero Extension and Metric Labelling under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from this area. Depending on the chosen cost function mu, we find that different algorithmic approaches can be applied to design FPT-algorithms: for arbitrary mu we parameterize by the number of edges that cross the cut (not the cost) and show how to solve Zero Extension in time O(|D|^{O(k^2)} n^4 log n) using randomized contractions. We improve this running time with respect to both parameter and input size to O(|D|^{O(k)} m) in the case where mu is a metric. We further show that the problem admits a polynomial sparsifier, that is, a kernel of size O(k^{|D|+1}) that is independent of the metric mu. With the stronger condition that mu is described by the distances of leaves in a tree, we parameterize by a gap parameter (q - p) between the cost of a true solution q and a `discrete relaxation' p and achieve a running time of O(|D|^{q-p} |T|m + |T|phi(n,m)) where T is the size of the tree over which mu is defined and phi(n,m) is the running time of a max-flow computation. We achieve a similar result for the more general Metric Labelling, while also allowing mu to be the distance metric between an arbitrary subset of nodes in a tree using tools from the theory of VCSPs. We expect the methods used in the latter result to have further applications.
Cite as

Felix Reidl and Magnus Wahlström. Parameterized Algorithms for Zero Extension and Metric Labelling Problems. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 94:1-94:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{reidl_et_al:LIPIcs.ICALP.2018.94,
  author =	{Reidl, Felix and Wahlstr\"{o}m, Magnus},
  title =	{{Parameterized Algorithms for Zero Extension and Metric Labelling Problems}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{94:1--94:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.94},
  URN =		{urn:nbn:de:0030-drops-90989},
  doi =		{10.4230/LIPIcs.ICALP.2018.94},
  annote =	{Keywords: FPT, VCSP, cut problem, gap parameter}
}
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