Improvement of one‐dimensional module placement in VLSI layout design

Abstract

AbstractThis paper considers the building block method, which is one of the methods in VLSI layout design, and discusses the improvement of module placement assuming that a one‐dimensional placement of the modules is given as the initial placement. Discussions are made of the following: The case where net list given as the input is composed only of two‐terminal nets, which connect the external terminals and the modules. The placement improvement problem PMO is formulated, where the virtual connection length defined only by × coordinate is to be minimized while retaining the placement order of the modules. The algorithm to solve this problem, as well as the proof for the optimality, are presented. Then a problem PM1 with a constraint on the range of displacement of the module is considered, and it is shown that the problem can be solved by extending the algorithm for PMO. A problem PM2 is considered, which is an extension of PM1 by introducing in general the multiterminal net connecting modules and external terminals. It is shown that PM2 can be reduced to PM1. A problem PM3 is considered, where river routing is adopted as the connection model, and the connection length is to be minimized considering also y coordinates (separation). It is shown that the optimal solution can be obtained in a polynomial time of the number of modules and the number of nets.