A Faster, Better Approximation Algorithm for the Minimum Latency Problem

We give a 7.18-approximation algorithm for the minimum latency problem that uses only O(n log n) calls to the prize-collecting Steiner tree (PCST) subroutine of Goemans and Williamson. This improves the previous best algorithms in both performance guarantee and running time. A previous algorithm of Goemans and Kleinberg for the minimum latency problem requires an approximation algorithm for the k-MST problem which is called as a black box for each value of k. Their algorithm can achieve an approximation factor of 10.77 while making O(n(n+log C) log n) PCST calls, a factor of 8.98 using O(n3 (n + log C) log n) PCST calls, or a factor of 7.18 + using nO(1/ ) log C PCST calls, via k-MST algorithms of Garg, Arya and Ramesh, and Arora and Karakostas, respectively. Here, n denotes the number of nodes in the instance, and C is the largest edge cost in the input. In all cases, the running time is dominated by the PCST calls. Since the PCST subroutine can be implemented to run in O(n2 ) time, ...

• Type: Journal
• Year: 2008
• Where: SIAMCOMP
• Authors: Aaron Archer, Asaf Levin, David P. Williamson
• Keywords: Algorithm, Approximation, Minimum Latency Problem, SIAMCOMP 2008