Approximation algorithms for network design problems on bounded subsets

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:36130

We address the problem of designing a network so that certain connectivity requirements are satisfied, at minimum cost of the edges used. The requirements are specified for each subset of vertices in terms of the number of edges with one endpoint in the set. We address a class of such problems where the connectivity is required for sets of bounded size, p. For this class of problems, we describe an O(log p)-approximation algorithm. We introduce a relaxation of the network design problem on directed graphs, where the requirement of each set is satisfied by the arcs that have their tails in the set. The relaxation allows arcs within the set to count towards the requirement of the set. We show that this relaxed problem is polynomial-time solvable if the requirement function is proper. The corresponding relaxation of the undirected problem is also polynomial-time solvable when the requirement function is proper. It is shown that in case the requirement function is not proper the relaxed version is NP-hard. The integer relaxed problem or its linear programming relaxation is used to produce an approximate solution to the network design problem.

• OSTI ID: 36130
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
COMPUTER NETWORKS
DESIGN
PARALLEL PROCESSING