Robust independence systems

Naonori Kakimura, Kazuhisa Makino

研究成果: Conference contribution

4 被引用数 (Scopus)

抄録

An independence system is one of the most fundamental combinatorial concepts, which includes a variety of objects in graphs and hypergraphs such as matchings, stable sets, and matroids. We discuss the robustness for independence systems, which is a natural generalization of the greedy property of matroids. For a real number α > 0, a set is said to be α-robust if for any k, it includes an α-approximation of the maximum k-independent set, where a set Y in is called k-independent if the size |Y| is at most k. In this paper, we show that every independence system has a -robust independent set, where denotes the exchangeability of . Our result contains a classical result for matroids and the ones of Hassin and Rubinstein,[12] for matchings and Fujita, Kobayashi, and Makino,[7] for matroid 2-intersections, and provides better bounds for the robustness for many independence systems such as b-matchings, hypergraph matchings, matroid p-intersections, and unions of vertex disjoint paths. Furthermore, we provide bounds of the robustness for nonlinear weight functions such as submodular and convex quadratic functions. We also extend our results to independence systems in the integral lattice with separable concave weight functions.

本文言語English
ホスト出版物のタイトルAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
ページ367-378
ページ数12
PART 1
DOI
出版ステータスPublished - 2011 7月 11
外部発表はい
イベント38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland
継続期間: 2011 7月 42011 7月 8

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
番号PART 1
6755 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other38th International Colloquium on Automata, Languages and Programming, ICALP 2011
国/地域Switzerland
CityZurich
Period11/7/411/7/8

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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