FAST-SP: a fast algorithm for block placement based on sequence pair

In this paper we present FAST-SP which is a fast block placement algorithm based on the sequence-pair placement representation. FAST-SP has two significant improvements over previous sequence-pair based placement algorithms: 1) FAST-SP translates each sequence pair to its corresponding block placement in O(n log log n) time based on a fast longest common subsequence computation. This is much faster than the traditional O(n²) method by first constructing horizontal and vertical constraint graphs and then performing longest path computations. As a result, FAST-SP can examine more sequence pairs and obtain a better placement solution in less runtime. 2) FAST-SP can handle placement constraints such as pre-placed constraint, range constraint, and boundary constraint. No previous sequence-pair based algorithms can handle range constraint and boundary constraint. Fast evaluation in O(n log log n) time is still valid in the presence of placement constraints and a novel cost function which unifies the evaluation of feasible and infeasible sequence pairs is used. We have implemented FAST-SP and obtained excellent experimental results. For all MCNC benchmark block placement problems, we have obtained the best results ever reported in the literature (including those reported by algorithms based on O-tree and B*-tree) with significantly less runtime. For example, the best known result for ami49 (36.8 mm²) was obtained by a B*-tree based algorithm using 4752 seconds, and FAST-SP obtained a better result (36.5 mm²) in 31 seconds.