Abstract
We generalize and unify techniques from several papers to obtain relatively simple and general technique for designing approximation algorithms for finding min-cost k-node connected spanning subgraphs. For the general instance of the problem, the previously best known algorithm has approximation ratio 2k. For k ≤ 5, algorithms with approximation ratio [(k+1)/2] are known. For metric costs Khuller and Raghavachari gave a (2 + 2(k−1)/n)-approximation algorithm. We obtain the following results. (i) An I(k−k0)-approximation algorithm for the problem of making a k0-connected graph k-connected by adding a minimum cost edge set, where I(k) = 2+ (eqution found). (ii) A (2 + k−1/n)-approximation algorithm for metric costs. (iv) A [(k + 1)/2]-approximation algorithm for k = 6, 7. (v) A fast [(k + 1)/2]-approximation algorithm for k = 4. The multiroot problem generalizes the min-cost k-connected subgraph problem. In the multiroot problem, requirements ku for every node u are given, and the aim is to find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u, v. For the general instance of the problem, the best known algorithm has approximation ratio 2k, where k = maxku. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for k ≤ 7 the approximation guarantee from 3 to 2 + [(k−1)/2]/k < 2.5.
Original language | English |
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Title of host publication | Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings |
Editors | Klaus Jansen, Samir Khuller |
Publisher | Springer Verlag |
Pages | 194-205 |
Number of pages | 12 |
ISBN (Electronic) | 9783540679967 |
DOIs | |
State | Published - 2000 |
Event | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, Germany Duration: 5 Sep 2000 → 8 Sep 2000 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1913 |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 |
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Country/Territory | Germany |
City | Saarbrucken |
Period | 5/09/00 → 8/09/00 |
Bibliographical note
Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2000.