Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On the red-blue set cover problem
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This paper presents approximation algorithms for two problems. First, a randomized algorithm guaranteeing approximation ratio √n with high probability is proposed for the Max-Rep problem of [Kor98], or the Label-CoverMAX problem (cf. [Hoc95]), where n is the number of vertices in the graph. This algorithm is then generalized into a 4√n- ratio algorithm for the nonuniform version of the problem. Secondly, it is shown that the Red-Blue Set Cover problem of [CDKM00] can be approximated with ratio 2√n log β, where n is the number of sets and β is the number of blue elements. Both algorithms can be adapted to the weighted variants of the respective problems, yielding the same approximation ratios.