Prize-collecting survivable network design in node-weighted graphs

Chandra Chekuri, Alina Ene, Ali Vakilian

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider node-weighted network design problems, in particular the survivable network design problem (SNDP) and its prize-collecting version (PC-SNDP). The input consists of a node-weighted undirected graph G = (V,E) and integral connectivity requirements r(st) for each pair of nodes st. The goal is to find a minimum node-weighted subgraph H of G such that, for each pair st, H contains r(st) edge-disjoint paths between s and t. PC-SNDP is a generalization in which the input also includes a penalty π(st) for each pair, and the goal is to find a subgraph H to minimize the sum of the weight of H and the sum of the penalties for all pairs whose connectivity requirements are not fully satisfied by H. Let k = max st r(st) be the maximum requirement. There has been no non-trivial approximation for node-weighted PC-SNDP for k > 1, the main reason being the lack of an LP relaxation based approach for node-weighted SNDP. In this paper we describe multiroute-flow based relaxations for the two problems and obtain approximation algorithms for PC-SNDP through them. The approximation ratios we obtain for PC-SNDP are similar to those that were previously known for SNDP via combinatorial algorithms. Specifically, we obtain an O(k 2 log n)-approximation in general graphs and an O(k 2)-approximation in graphs that exclude a fixed minor. The approximation ratios can be improved by a factor of k but the running times of the algorithms depend polynomially on n k.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings
Pages98-109
Number of pages12
DOIs
StatePublished - Aug 28 2012
Event15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 - Cambridge, MA, United States
Duration: Aug 15 2012Aug 17 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7408 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
CountryUnited States
CityCambridge, MA
Period8/15/128/17/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Chekuri, C., Ene, A., & Vakilian, A. (2012). Prize-collecting survivable network design in node-weighted graphs. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings (pp. 98-109). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7408 LNCS). https://doi.org/10.1007/978-3-642-32512-0_9