A polynomial algorithm for b-matchings: an alternative approach
Information Processing Letters
SIAM Journal on Discrete Mathematics
Greedy local improvement and weighted set packing approximation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
An Optimal Deterministic Algorithm for Online b-Matching
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Approximation Algorithms for Channel Assignment in Cellular Radio Networks
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
Solving the Weighted Parity Problem for Gammoids by Reduction to
Solving the Weighted Parity Problem for Gammoids by Reduction to
Matching algorithms.
On the complexity of approximating k-set packing
Computational Complexity
Greedy in approximation algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
Mathematics of Operations Research
Constrained non-monotone submodular maximization: offline and secretary algorithms
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Nonmonotone submodular maximization via a structural continuous greedy algorithm
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
A Unified Continuous Greedy Algorithm for Submodular Maximization
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
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Submodular maximization and set systems play a major role in combinatorial optimization. It is long known that the greedy algorithm provides a 1/(k + 1)-approximation for maximizing a monotone submodular function over a k-system. For the special case of k-matroid intersection, a local search approach was recently shown to provide an improved approximation of 1/(k +δ) for arbitrary δ 0. Unfortunately, many fundamental optimization problems are represented by a k-system which is not a k-intersection. An interesting question is whether the local search approach can be extended to include such problems. We answer this question affirmatively. Motivated by the b-matching and k-set packing problems, as well as the more general matroid k-parity problem, we introduce a new class of set systems called k-exchange systems, that includes k-set packing, b-matching, matroid k-parity in strongly base orderable matroids, and additional combinatorial optimization problems such as: independent set in (k+1)-claw free graphs, asymmetric TSP, job interval selection with identical lengths and frequency allocation on lines. We give a natural local search algorithm which improves upon the current greedy approximation, for this new class of independence systems. Unlike known local search algorithms for similar problems, we use counting arguments to bound the performance of our algorithm. Moreover, we consider additional objective functions and provide improved approximations for them as well. In the case of linear objective functions, we give a non-oblivious local search algorithm, that improves upon existing local search approaches for matroid k-parity.