Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Algorithmic Chernoff-Hoeffding inequalities in integer programming
Random Structures & Algorithms
Tight approximations for resource constrained scheduling and bin packing
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
An extension of the Lovász local lemma, and its applications to integer programming
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New Algorithmic Aspects of the Local Lemma with Applications to Routing and Partitioning
SIAM Journal on Computing
Deterministic Hypergraph Coloring and Its Applications
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
The lovász-local-lemma and scheduling
Efficient Approximation and Online Algorithms
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We consider the design of approximation algorithms for multicolor generalization of the well known hypergraph 2-coloring problem (property B). Consider a hypergraph H with n vertices, s edges, maximum edge degree D(驴 s) and maximum vertex degree d(驴 s). We study the problem of coloring the vertices of H with minimum number of colors such that no hyperedge i contains more than bi vertices of any color. The main result of this paper is a deterministic polynomial time algorithm for constructing approximate, 驴(1 + 驴)OPT驴-colorings (驴 驴 (0, 1)) satisfying all constraints provided that bi's are logarithmically large in d and two other parameters. This approximation ratio is independent of s. Our lower bound on the bi's is better than the previous best bound. Due to the similarity of structure these methods can also be applied to resource constrained scheduling. We observe, using the non-approximability result for graph coloring of Feige and Killian[4], that unless NP 驴 ZPP we cannot find a solution with approximation ratio s1/2-驴 in polynomial time, for any fixed small 驴 0.