An Investigation into Statistical Properties of Partitioning and Floorplanning Problems

In this paper we examine some statistical properties exhibited by combinatorial optimization problems. Although the paper focuses on two particular problems that arise in chip design, namely circuit partitioning and floorplanning, the results seem valid for a much larger set of such problems. For the partitioning problem, we examine the solutions generated by the well known Kernighan-Lin procedure [5] [10] and solutions generated by random search. We find that in both cases, the Type 3 (Weibull) extreme-value distribution provides an excellent model for the distribution of local minima generated. The location parameter of the Weibull provides an estimate of the minimum cost. For the floorplanning problem, we construct a number of test problems, whose optimal value is known. As with the partitioning problem, we find that the Weibull distribution provides an excellent model for estimating the minimum cost.