File transfer tree problems

Abstract

Given an edge-weighted digraph G with a designated vertex r, and a vertex capacity σ, we consider the problem of finding a shortest path tree T rooted at r such that for each vertex v the number of children of v in T does not exceed the capacity σ(v). The problem has an application in designing a routing for transferring files from the source node to other nodes in an information network. In this paper, we first present an efficient algorithm to the problem. We then introduce extensions of the problem by relaxing the degree constraint or the distance constraint in various ways and show polynomial algorithms or the computational hardness of these problems. © Springer-Verlag Berlin Heidelberg 2002.