An effective structured approach to finding optimal partitions of networks

Abstract

The problem considered is to partition an edge-valued, node-weighted, finite, connected, simple graph (called a network) into disjoint subgraphs, each of which has a total node weight that does not exceed a weight constraint, and so that the total value of edges interconnecting the subgraphs is minimized. This paper presents a new approach which is effective in solving the problem, and fast enough to be practical in finding optimal partitions of large networks. It uses the concept of “divide and conquer” to partition the problem into several subproblems, which can be efficiently solved one after the other by using depth-first search and branch-and-bound principle. The operations required under the algorithms are additions, comparisons, and logical operations on binary vectors.