O(n log2 n) an algorithm for a sink location problem in dynamic tree networks

Abstract

In this paper, we consider a sink location in a dynamic network which consists of a graph with capacities and transit times on its arcs. Given a dynamic network with initial supplies at vertices, the problem is to find a vertex as a sink in the network such that we can send all the initial supplies to as quickly as possible. We present an O(n log2 n) time algorithm for the sink location problem in a dynamic network of tree structure, where n is the number of vertices in the network. This improves upon the existing O(n2)-time bound. As a corollary, we also show that the quickest transshipment problem can be solved in O(n log2 n) time if a given network is a tree and has a single sink. Our results are based on data structures for representing tables (i.e., sets of intervals with their height), which may be of independent interest. © 2004 Springer Science + Business Media, Inc.