Approximating the k-traveling repairman problem with repairtimes

Given an undirected graph G = (V,E) and a source vertex s ∈ V , the k-traveling repairman (KTR) problem, also known as the minimum latency problem, asks for k tours, each starting at s and together covering all the vertices (customers) such that the sum of the latencies experienced by the customers is minimum. The latency of a customer p is defined to be the distance traveled (time elapsed) before visiting p for the first time. Previous literature on the KTR problem has considered the version of the problem in which the repairtime of a customer is assumed to be zero for latency calculations. We consider a generalization of the problem in which each customer has an associated repairtime. For a fixed k, we present a (β + 2)-approximation algorithm for this problem, where β is the best achievable approximation ratio for the KTR problem with zero repairtimes (currently β = 6). For arbitrary k, we obtain a (3 2 β + 1 2 )-approximation ratio. When the repairtimes of the customers a...

• Type: Journal
• Year: 2007
• Where: JDA
• Authors: Raja Jothi, Balaji Raghavachari
• Keywords: Customer, JDA 2007, KTR Problem, Minimum Latency Problem