Improved Approximation Algorithms for the Minimum Latency Problem via Prize-Collecting Strolls

The minimum latency problem (MLP) is a well-studied variant of the traveling salesman problem (TSP). In the MLP, the server's goal is to minimize the average latency that the clients experience prior to being served, rather than the total latency experienced by the server (as in the TSP). The MLP sometimes goes by other names, such as the traveling repairman problem, or the deliveryman problem. Unlike most combinatorial optimization problems, the MLP is NP-hard even on trees (Sitters, 2001). Our main result is an improved approximation algorithm for the MLP on trees, upon which we build improved approximation algorithms for a much wider class of graphs. The MLP on trees is interesting for several reasons. First, many of the aspects that make the problem difficult on general graphs are already present in the tree case. Second, all existing approximation algorithms for general graphs are built on approximation algorithms for the tree case. Third, there has been no improvement for t...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Aaron Archer, Anna Blasiak
• Keywords: Discrete Algorithms, General Graphs, Improved Approximation Algorithm, Minimum Latency Problem, SODA 2010