Robust independence systems

Naonori Kakimura, Kazuhisa Makino

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
Pages367-378
Number of pages12
Volume6755 LNCS
EditionPART 1
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland
Duration: 2011 Jul 42011 Jul 8

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6755 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

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

Fingerprint

Independence System
Matroid
Independent Set
Robustness
Hypergraph
Weight Function
Intersection
Exchangeability
Stable Set
Disjoint Paths
Concave function
Quadratic Function
Nonlinear Function
Convex function
Union
Denote
Approximation
Graph in graph theory
Vertex of a graph

Keywords

  • exchangeability
  • independence systems
  • matroids
  • robustness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kakimura, N., & Makino, K. (2011). Robust independence systems. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings (PART 1 ed., Vol. 6755 LNCS, pp. 367-378). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-22006-7_31

Robust independence systems. / Kakimura, Naonori; Makino, Kazuhisa.

Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. Vol. 6755 LNCS PART 1. ed. 2011. p. 367-378 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kakimura, N & Makino, K 2011, Robust independence systems. in Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 edn, vol. 6755 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6755 LNCS, pp. 367-378, 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, Zurich, Switzerland, 11/7/4. https://doi.org/10.1007/978-3-642-22006-7_31
Kakimura N, Makino K. Robust independence systems. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 ed. Vol. 6755 LNCS. 2011. p. 367-378. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-642-22006-7_31
Kakimura, Naonori ; Makino, Kazuhisa. / Robust independence systems. Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. Vol. 6755 LNCS PART 1. ed. 2011. pp. 367-378 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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