Greedy local improvement and weighted set packing approximation
Journal of Algorithms
SIAM Journal on Discrete Mathematics
SIAM Journal on Computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
Graphs, Networks and Algorithms (Algorithms and Computation in Mathematics)
Robust subgraphs for trees and paths
ACM Transactions on Algorithms (TALG)
Greedy in approximation algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Robust matchings and matroid intersections
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
A General Approach for Incremental Approximation and Hierarchical Clustering
SIAM Journal on Computing
Computing knapsack solutions with cardinality robustness
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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An independence system F 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 X ∈ F 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 F is called k-independent if the size |Y| is at most k. In this paper, we show that every independence system has a 1/√µ(F)-robust independent set, where µ(F) denotes the exchangeability of F. 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.