An O(n2 log2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks.

We consider the problem of locating a set of k sinks on a path network with general edge capacities that minimizes the sum of the evacuation times of all evacuees. We first present an O ( k n log 4 ⁡ n ) time algorithm when the edge capacities are non-uniform, where n is the number of vertices. We then present an O ( k n log 3 ⁡ n ) time algorithm when the edge capacities are uniform. We also present an O ( n log ⁡ n ) time algorithm for the special case where k = 1 and the edge capacities are non-uniform.