4 Search Results for "Huang, Shenwei"

Document
DOI: 10.4230/LIPIcs.ESA.2024.82
A Lower Bound for Local Search Proportional Approval Voting

Authors: Sonja Kraiczy and Edith Elkind

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

Abstract
Selecting k out of m items based on the preferences of n heterogeneous agents is a widely studied problem in algorithmic game theory. If agents have approval preferences over individual items and harmonic utility functions over bundles - an agent receives ∑_{j = 1}^t1/j utility if t of her approved items are selected - then welfare optimisation is captured by a voting rule known as Proportional Approval Voting (PAV). PAV also satisfies demanding fairness axioms. However, finding a winning set of items under PAV is NP-hard. In search of a tractable method with strong fairness guarantees, a bounded local search version of PAV was proposed [Aziz et al., 2018]. It proceeds by starting with an arbitrary size-k set W and, at each step, checking if there is a pair of candidates a ∈ W, b ̸ ∈ W such that swapping a and b increases the total welfare by at least ε; if yes, it performs the swap. Aziz et al. show that setting ε = n/(k²) ensures both the desired fairness guarantees and polynomial running time. However, they leave it open whether the algorithm converges in polynomial time if ε is very small (in particular, if we do not stop until there are no welfare-improving swaps). We resolve this open question, by showing that if ε can be arbitrarily small, the running time of this algorithm may be super-polynomial. Specifically, we prove a lower bound of Ω(k^{log k}) if improvements are chosen lexicographically. To complement our lower bound, we provide an empirical comparison of two variants of local search - better-response and best-response - on several real-life data sets and a variety of synthetic data sets. Our experiments indicate that, empirically, better response exhibits faster running time than best response.
Cite as

Sonja Kraiczy and Edith Elkind. A Lower Bound for Local Search Proportional Approval Voting. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 82:1-82:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kraiczy_et_al:LIPIcs.ESA.2024.82,
  author =	{Kraiczy, Sonja and Elkind, Edith},
  title =	{{A Lower Bound for Local Search Proportional Approval Voting}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{82:1--82:14},
  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.2024.82},
  URN =		{urn:nbn:de:0030-drops-211538},
  doi =		{10.4230/LIPIcs.ESA.2024.82},
  annote =	{Keywords: Computational Social Choice, Committee Elections, Local Search, Fairness}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.55
Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes

Authors: Jan Goedgebeur, Jorik Jooken, Karolina Okrasa, Paweł Rzążewski, and Oliver Schaudt

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

Abstract
For graphs G and H, an H-coloring of G is an edge-preserving mapping from V(G) to V(H). Note that if H is the triangle, then H-colorings are equivalent to 3-colorings. In this paper we are interested in the case that H is the five-vertex cycle C₅. A minimal obstruction to C₅-coloring is a graph that does not have a C₅-coloring, but every proper induced subgraph thereof has a C₅-coloring. In this paper we are interested in minimal obstructions to C₅-coloring in F-free graphs, i.e., graphs that exclude some fixed graph F as an induced subgraph. Let P_t denote the path on t vertices, and let S_{a,b,c} denote the graph obtained from paths P_{a+1},P_{b+1},P_{c+1} by identifying one of their endvertices. We show that there is only a finite number of minimal obstructions to C₅-coloring among F-free graphs, where F ∈ {P₈, S_{2,2,1}, S_{3,1,1}} and explicitly determine all such obstructions. This extends the results of Kamiński and Pstrucha [Discr. Appl. Math. 261, 2019] who proved that there is only a finite number of P₇-free minimal obstructions to C₅-coloring, and of Dębski et al. [ISAAC 2022 Proc.] who showed that the triangle is the unique S_{2,1,1}-free minimal obstruction to C₅-coloring. We complement our results with a construction of an infinite family of minimal obstructions to C₅-coloring, which are simultaneously P_{13}-free and S_{2,2,2}-free. We also discuss infinite families of F-free minimal obstructions to H-coloring for other graphs H.
Cite as

Jan Goedgebeur, Jorik Jooken, Karolina Okrasa, Paweł Rzążewski, and Oliver Schaudt. Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goedgebeur_et_al:LIPIcs.MFCS.2024.55,
  author =	{Goedgebeur, Jan and Jooken, Jorik and Okrasa, Karolina and Rz\k{a}\.{z}ewski, Pawe{\l} and Schaudt, Oliver},
  title =	{{Minimal Obstructions to C₅-Coloring in Hereditary Graph Classes}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.55},
  URN =		{urn:nbn:de:0030-drops-206110},
  doi =		{10.4230/LIPIcs.MFCS.2024.55},
  annote =	{Keywords: graph homomorphism, critical graphs, hereditary graph classes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.31
Complexity of C_k-Coloring in Hereditary Classes of Graphs

Authors: Maria Chudnovsky, Shenwei Huang, Paweł Rzążewski, Sophie Spirkl, and Mingxian Zhong

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f:V(G) -> V(H) such that for every edge uv in E(G) it holds that f(u)f(v)in E(H). We are interested in the complexity of the problem H-Coloring, which asks for the existence of an H-coloring of an input graph G. In particular, we consider H-Coloring of F-free graphs, where F is a fixed graph and H is an odd cycle of length at least 5. This problem is closely related to the well known open problem of determining the complexity of 3-Coloring of P_t-free graphs. We show that for every odd k >= 5 the C_k-Coloring problem, even in the precoloring-extension variant, can be solved in polynomial time in P_9-free graphs. On the other hand, we prove that the extension version of C_k-Coloring is NP-complete for F-free graphs whenever some component of F is not a subgraph of a subdivided claw.
Cite as

Maria Chudnovsky, Shenwei Huang, Paweł Rzążewski, Sophie Spirkl, and Mingxian Zhong. Complexity of C_k-Coloring in Hereditary Classes of Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chudnovsky_et_al:LIPIcs.ESA.2019.31,
  author =	{Chudnovsky, Maria and Huang, Shenwei and Rz\k{a}\.{z}ewski, Pawe{\l} and Spirkl, Sophie and Zhong, Mingxian},
  title =	{{Complexity of C\underlinek-Coloring in Hereditary Classes of Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.31},
  URN =		{urn:nbn:de:0030-drops-111529},
  doi =		{10.4230/LIPIcs.ESA.2019.31},
  annote =	{Keywords: homomorphism, hereditary class, computational complexity, forbidden induced subgraph}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.35
Colouring Square-Free Graphs without Long Induced Paths

Authors: Serge Gaspers, Shenwei Huang, and Daniel Paulusma

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
The Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a given integer k such that no two adjacent vertices are coloured alike. The complexity of Colouring is fully understood for graph classes characterized by one forbidden induced subgraph H. Despite a huge body of existing work, there are still major complexity gaps if two induced subgraphs H_1 and H_2 are forbidden. We let H_1 be the s-vertex cycle C_s and H_2 be the t-vertex path P_t. We show that Colouring is polynomial-time solvable for s=4 and t<=6, which unifies several known results for Colouring on (H_1,H_2)-free graphs. Our algorithm is based on a novel decomposition theorem for (C_4,P_6)-free graphs without clique cutsets into homogeneous pairs of sets and a new framework for bounding the clique-width of a graph by the clique-width of its subgraphs induced by homogeneous pairs of sets. To apply this framework, we also need to use divide-and-conquer to bound the clique-width of subgraphs induced by homogeneous pairs of sets. To complement our positive result we also prove that Colouring is NP-complete for s=4 and t>=9, which is the first hardness result on Colouring for (C_4,P_t)-free graphs.
Cite as

Serge Gaspers, Shenwei Huang, and Daniel Paulusma. Colouring Square-Free Graphs without Long Induced Paths. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gaspers_et_al:LIPIcs.STACS.2018.35,
  author =	{Gaspers, Serge and Huang, Shenwei and Paulusma, Daniel},
  title =	{{Colouring Square-Free Graphs without Long Induced Paths}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.35},
  URN =		{urn:nbn:de:0030-drops-84922},
  doi =		{10.4230/LIPIcs.STACS.2018.35},
  annote =	{Keywords: graph colouring, hereditary graph class, clique-width, cycle, path}
}
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