Greedy algorithm and symmetric matroids
Mathematical Programming: Series A and B
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Journal of Algebraic Combinatorics: An International Journal
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
A framework for the greedy algorithm
Discrete Applied Mathematics
A simple approximation algorithm for the weighted matching problem
Information Processing Letters
Approximating asymmetric maximum TSP
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Limited-Backtrack Greedy Schema for Approximation Algorithms
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
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A simpler linear time 2/3 - ε approximation for maximum weight matching
Information Processing Letters
Linear time 1/2 -approximation algorithm for maximum weighted matching in general graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Truthful Mechanisms via Greedy Iterative Packing
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Matroid matching: the power of local search
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Price of anarchy for greedy auctions
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Characterizing problems for realizing policies in self-adaptive and self-managing systems
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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
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The objective of this paper is to characterize classes of problems for which a greedy algorithm finds solutions provably close to optimum. To that end, we introduce the notion of k-extendible systems, a natural generalization of matroids, and show that a greedy algorithm is a 1/k-factor approximation for these systems. Many seemly unrelated problems fit in our framework, e.g.: b-matching, maximum profit scheduling and maximum asymmetric TSP. In the second half of the paper we focus on the maximum weight b- atching problem. The problem forms a 2-extendible system, so greedy gives us a 1/2 -factor solution which runs in O(m logn) time. We improve this by providing two linear time approximation algorithms for the problem: a 1/2 -factor algorithm that runs in O(b m) time, and a (2/3- ε) -factor algorithm which runs in expected O(bm log 1/ε) time.