Minimax Regret k-sink Location Problem in Dynamic Path Networks

This paper considers minimax regret 1-sink location problems in dynamic path networks. A dynamic path network consists of an undirected path with positive edge lengths and constant edge capacity and the vertex supply which is nonnegative value, called weight, is unknown but only the interval of weight is known. A particular assignment of weight to each vertex is called a scenario. Under any scenario, the cost of a sink is defined as the minimum time to complete evacuation for all weights (evacuees), and the regret of a sink location x is defined as the cost of x minus the cost of an optimal sink. Then, the problem is to find a point as a sink such that the maximum regret for all possible scenarios is minimized. We present an O(n log n) time algorithm for minimax regret 1-sink location problems in dynamic path networks, where n is the number of vertices in the network.