 
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
fageev,svirg@math.nsc.ru
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.
