Speedup in the Traveling Repairman Problem with Unit Time Windows

The input to the unrooted traveling repairman problem is an undirected metric graph and a subset of nodes, each of which has a time window of unit length. Given that a repairman can start at any location, the goal is to plan a route that visits as many nodes as possible during their respective time windows. A polynomial-time bicriteria approximation algorithm is presented for this problem, gaining an increased fraction of repairman visits for increased speedup of repairman motion. For speedup s, we find a 6γ/(s+ 1)-approximation for s in the range 1 ≤ s ≤ 2 and a 4γ/s-approximation for s in the range 2 ≤ s ≤ 4, where γ = 1 on tree-shaped networks and γ = 2 + ǫ on general metric graphs.