3 Search Results for "Fu, Bin"

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.122

An Improved Integrality Gap for Disjoint Cycles in Planar Graphs

Authors: Niklas Schlomberg

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

Abstract

We present a new greedy rounding algorithm for the Cycle Packing Problem for uncrossable cycle families in planar graphs. This improves the best-known upper bound for the integrality gap of the natural packing LP to a constant slightly less than 3.5. Furthermore, the analysis works for both edge- and vertex-disjoint packing. The previously best-known constants were 4 for edge-disjoint and 5 for vertex-disjoint cycle packing. This result also immediately yields an improved Erdős-Pósa ratio: for any uncrossable cycle family in a planar graph, the minimum number of vertices (edges) needed to hit all cycles in the family is less than 8.38 times the maximum number of vertex-disjoint (edge-disjoint, respectively) cycles in the family. Some uncrossable cycle families of interest to which the result can be applied are the family of all cycles in a directed or undirected graph, in undirected graphs also the family of all odd cycles and the family of all cycles containing exactly one edge from a specified set of demand edges. The last example is an equivalent formulation of the fully planar Disjoint Paths Problem. Here the Erdős-Pósa ratio translates to a ratio between integral multi-commodity flows and minimum cuts.

Cite as

Niklas Schlomberg. An Improved Integrality Gap for Disjoint Cycles in Planar Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 122:1-122:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schlomberg:LIPIcs.ICALP.2024.122,
  author =	{Schlomberg, Niklas},
  title =	{{An Improved Integrality Gap for Disjoint Cycles in Planar Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{122:1--122:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.122},
  URN =		{urn:nbn:de:0030-drops-202651},
  doi =		{10.4230/LIPIcs.ICALP.2024.122},
  annote =	{Keywords: Cycle packing, planar graphs, disjoint paths}
}

Document

DOI: 10.4230/DagMan.10.1.1

Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.

Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2018.31

New Algorithms for Edge Induced König-Egerváry Subgraph Based on Gallai-Edmonds Decomposition

Authors: Qilong Feng, Guanlan Tan, Senmin Zhu, Bin Fu, and Jianxin Wang

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract

König-Egerváry graphs form an important graph class which has been studied extensively in graph theory. Much attention has also been paid on König-Egerváry subgraphs and König-Egerváry graph modification problems. In this paper, we focus on one König-Egerváry subgraph problem, called the Maximum Edge Induced König Subgraph problem. By exploiting the classical Gallai-Edmonds decomposition, we establish connections between minimum vertex cover, Gallai-Edmonds decomposition structure, maximum matching, maximum bisection, and König-Egerváry subgraph structure. We obtain a new structural property of König-Egerváry subgraph: every graph G=(V, E) has an edge induced König-Egerváry subgraph with at least 2|E|/3 edges. Based on the new structural property proposed, an approximation algorithm with ratio 10/7 for the Maximum Edge Induced König Subgraph problem is presented, improving the current best ratio of 5/3. To the best of our knowledge, this paper is the first one establishing the connection between Gallai-Edmonds decomposition and König-Egerváry graphs. Using 2|E|/3 as a lower bound, we define the Edge Induced König Subgraph above lower bound problem, and give a kernel of at most 30k edges for the problem.

Cite as

Qilong Feng, Guanlan Tan, Senmin Zhu, Bin Fu, and Jianxin Wang. New Algorithms for Edge Induced König-Egerváry Subgraph Based on Gallai-Edmonds Decomposition. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 31:1-31:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{feng_et_al:LIPIcs.ISAAC.2018.31,
  author =	{Feng, Qilong and Tan, Guanlan and Zhu, Senmin and Fu, Bin and Wang, Jianxin},
  title =	{{New Algorithms for Edge Induced K\"{o}nig-Egerv\'{a}ry Subgraph Based on Gallai-Edmonds Decomposition}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{31:1--31:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.31},
  URN =		{urn:nbn:de:0030-drops-99790},
  doi =		{10.4230/LIPIcs.ISAAC.2018.31},
  annote =	{Keywords: K\"{o}nig-Egerv\'{a}ry graph, Gallai-Edmonds decomposition}
}

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1 Delgrande, James P.
1 Feng, Qilong
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2 Mathematics of computing → Approximation algorithms
1 Computing methodologies → Artificial intelligence
1 Computing methodologies → Knowledge representation and reasoning
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1 Applications of logics
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