### 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 language | English |
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Title of host publication | Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings |

Pages | 367-378 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

Publication status | Published - 2011 Jul 11 |

Externally published | Yes |

Event | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland Duration: 2011 Jul 4 → 2011 Jul 8 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 6755 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 |
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Country | Switzerland |

City | Zurich |

Period | 11/7/4 → 11/7/8 |

### Keywords

- exchangeability
- independence systems
- matroids
- robustness

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings*(PART 1 ed., 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