On complexity of a message-routing strategy for multicomputer systems

Abstract

A natural communication problem in a multicomputer system, such as the hypercube, is that a processor (called the source) wants to send a message to a number of other processors (destinations). A message-routing paradigm for such a multidestination communication has been formulated as finding a subgraph called an optimal distance-preserving tree (ODPT). We prove that the problem of finding an ODPT is NP-hard both for the n-cube graph as well as for a graph whose maximum degree is at most three.