A linear arrangement problem with applications
A linear arrangement problem, called the minmax mincut problem, emerging from circuit design is investigated. Its input is a series-parallel directed hypergraph, and the output is a linear arrangement (and a layout). The primary objective is to minimize the longest path, and the secondary objective is to minimize the cutwidth. It is shown that cutwidth D, subject to longest path minimization, is affected by pattern number k, which is also a lower bound on the cutwidth but not a tight one. There exist examples with k=/spl Omega/(N), where N is the number of vertices. We propose an algorithm producing cutwidths D=O(k+log N). We also show that every series-parallel directed hypergraph, after reordering the serial paths, can be linearly placed with cutwidth D=O(log N). Simultaneously, its dual series-parallel directed hypergraph can be linearly placed with the same vertex order and with cutwidth D=O(log N). Applications on gate-matrix layout style in very large-scale-integrated (VLSI) CMOS circuit design are demonstrated.