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On-line and Off-line Approximation Algorithms for Vector Covering Problems
 

Summary: On-line and Off-line Approximation Algorithms
for Vector Covering Problems
Noga Alon
Yossi Azar
J´anos Csirik
Leah Epstein §
Sergey V. Sevastianov ¶
Arjen P.A. Vestjens
Gerhard J. Woeginger
Abstract
This paper deals with vector covering problems in d-dimensional space. The input to
a vector covering problem consists of a set X of d-dimensional vectors in [0, 1]d
. The goal
is to partition X into a maximum number of parts, subject to the constraint that in every
part the sum of all vectors is at least one in every coordinate. This problem is known to be
NP-complete, and we are mainly interested in its on-line and off-line approximability.
For the on-line version, we construct approximation algorithms with worst case guarantee
arbitrarily close to 1/(2d) in d 2 dimensions. This result contradicts a statement of Csirik
and Frenk (1990) in [5] where it is claimed that for d 2, no on-line algorithm can have a
worst case ratio better than zero. Moreover, we prove that for d 2, no on-line algorithm can

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics