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Approximation Algorithms for Maximum Coverage and Max Cut with Given Sizes of

Summary: Approximation Algorithms for Maximum
Coverage and Max Cut with Given Sizes of
Parts ?
A. A. Ageev and M. I. Sviridenko
Sobolev Institute of Mathematics
pr. Koptyuga 4, 630090, Novosibirsk, Russia
Abstract. In this paper we demonstrate a general method of designing
constant­factor 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 \Gamma (1 \Gamma 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=2­approximation 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 well­known (1 \Gamma e \Gamma1 )­greedy algorithm due to Cornuejols, Fisher
and Nemhauser in each case of bounded k. The latter is, to the best of
our knowledge, the first constant­factor algorithm for that version of the
maximum cut problem.


Source: Ageev, Alexandr - Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk


Collections: Mathematics