Resource placement in Cartesian product of networks

Abstract

The utilization of the limited resources of a multiprocessor or multicomputer system is a primary performance issue which is crucial for the design of many scheduling algorithms. While many of the existing parallel machines benefit from a regular product network topology, almost none of the previous resource placement techniques have come to recognize and exploit this inherent regularity. This paper introduces several novel algorithms for deriving resource placement schemes in product networks based on the assumption of perfect resource placement in their underling basic graphs. Our techniques use known schemes for the basic networks as their building blocks for deploying the resource placement scheme in the product network. This seriously cuts down the expenses required for deploying and rescaling the network. In particular, we propose some efficient algorithms for adjacency placement in a product of k heterogeneous graphs. Furthermore, we extend our approach and present algorithms for distant resource placement in product networks.