Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of Parts
نویسندگان
چکیده
In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic (\pipage") procedure of rounding of linear relaxations. By using the method we design a (1 ? (1 ? 1=k) k)-approximation algorithm for the maximum coverage problem where k is the maximum size of the subsets that are covered, and a 1=2-approximation algorithm for the maximum cut problem with given sizes of parts in the vertex set bipartition. The performance guarantee of the former improves on that of the well-known (1 ? e ?1)-greedy algorithm due to Cornuejols, Fisher and Nemhauser in each case of bounded k. The latter is, to the best of our knowledge, the rst constant-factor algorithm for that version of the maximum cut problem.
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