Minmax-cut graph partitioning problems

Two partitioning problems on graphs are considered. In the first problem the nodes of a directed graph are partitioned into sets of sizes within prescribed ranges. If in(V/sub i/) is the sum of the weights on the incoming edges to set V/sub i/ in the partition, the goal is to minimize max/sub i/ (in(V/sub i/)). It is shown that the problem is NP-hard if the maximum set size is at least three or there is a constant number of sets of the same size. For the case where n and m are the number of nodes and the number of edges of the input graph, respectively, an O(m square root n) time algorithm is obtained when the maximum set size is two. The same problem is then considered on undirected graphs. It is shown that this partitioning problem is NP-hard for partitioning into equal-size sets, but polynomial-time algorithms are obtained when the maximum set size is a constant k. Applications of the problems are in layout, built-in self-test (BIST), and high-level synthesis.<<ETX>>