Abstract

Domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems. In the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain, domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly. Motivated by this fact, we study the following min--max boundary multi--way partitioning problem: Given a graph G and an integer k ? 1, we would like to divide G into k subgraphs G 1 ; : : : ; G k (by removing edges) such that (i) jG i j = \Theta(jGj=k) for all i 2 f1; : : : ; kg; and (ii) the maximum boundary size of any subgraph (the set of edges connecting it with other subgraphs) is minimized. We provide an algorithm that given G, a well--shaped mesh in d dimensions, finds a partition of G into k subgraphs G 1 ; : : : ; G k , such that for all i, G i has \Theta(jGj=k) vertices and the number of edges connecting G i with the ot...

Citations