Faster approximation algorithms 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 a performance guarantee of 10.77 while making O(n2 log n) PCST calls (via a k-MST algorithm of Garg), or a performance guarantee of 7.18+ while using nO(1/ ) PCST calls (via a k-MST algorithm of Arora and Karakostas). 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, the overall running time of our algorithm is O(n3 log n). The basic idea for our improvement is that we do not treat the k-MST algorithm as a black box. This ...

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Aaron Archer, David P. Williamson
• Keywords: Algorithm, Algorithms, Minimum Latency Problem, Performance Guarantee, SODA 2003