Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Asymptotic packing via a branching process
Random Structures & Algorithms
Asymptotic packing and the random greedy algorithm
Random Structures & Algorithms
Randomized greedy matching. II
Random Structures & Algorithms
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
Tight approximations for resource constrained scheduling and bin packing
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
Optimal solutions for multi-unit combinatorial auctions: branch and bound heuristics
Proceedings of the 2nd ACM conference on Electronic commerce
IBM Journal of Research and Development
On the complexity of approximating k-set packing
Computational Complexity
Greedy approximation via duality for packing, combinatorial auctions and routing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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We consider the b -matching problem in a hypergraph on n vertices and edge cardinality bounded by ***. Oblivious greedy algorithms achieve approximations of $(\sqrt{n}+1)^{-1}$ and (*** + 1)*** 1 independently of b (Krysta 2005). Randomized rounding achieves constant-factor approximations of 1 *** *** for large b , namely b = *** (*** *** 2, ln n ), (Srivastav and Stangier 1997). Hardness of approximation results exist for b = 1 (Gonen and Lehmann 2000; Hazan, Safra, and Schwartz 2006). In the range of 1 b *** ln n , no close-to-one, or even constant-factor, polynomial-time approximations are known. The aim of this paper is to overcome this algorithmic stagnation by proposing new algorithms along with the first experimental study of the b -matching problem in hypergraphs, and to provide a first theoretical analysis of these algorithms to some extent. We propose a non-oblivious greedy algorithm and a hybrid algorithm combining randomized rounding and non-oblivious greedy. Experiments on random and real-world instances suggest that the hybrid can, in terms of approximation, outperform the known techniques. The non-oblivious greedy also shows a better approximation in many cases than the oblivious one and is accessible to theoretic analysis.