On the power of logic resynthesis

A linear arrangement problem, called the minmax mincut problem, emerging fr om circuit design is investigated. Its input is a series-parallel directed hypergraph (SPDH), and the output is a linear arrangement (and a layout). T he primary objective is to minimize the longest path, and the secondary obj ective is to minimize the cutwidth. It is shown that cutwidth D, subject to longest path minimization, is affected by two terms: pattern number k and balancing number m. Also, k and m are both lower bounds on the cutwidth. An algorithm, running in linear time, produces layouts with cutwidths D less than or equal to 2(k + m). There exist examples with k = Omega(N), where N is the number of vertices; however, m is always O(log N). We show that ever y SPDH, after local logic resynthesis (specifically, after reordering the s erial paths), can be linearly placed with cutwidth D = O(log N). Simultaneo usly, its dual SPDH can be linearly placed with the same vertex order and w ith cutwidth D = O(log N). Therefore, after local resynthesis the area can be reduced by a factor of N/log N. Application to gate-matrix layout style is demonstrated.