We present a genetic algorithm (GA) that uses a slicing tree construction process for the placement and area optimization of soft modules in very large scale integration floorplan design. We have overcome the serious representational problems usually associated with encoding slicing floorplans into GAs, and have obtained excellent (often optimal) results for module sets with up to 100 rectangles. The slicing tree construction process used by our GA to generate the floorplans has a run-time scaling of O(n lg n). This compares very favourably with other recent approaches based on non-slicing floorplans that require much longer run times. We demonstrate that our GA outperforms a simulated annealing implementation with the same representation and mutation operators as the GA.
This paper summarizes the results of a preliminary study that examines the feasibility of implementing computer algebra systems on massively pamllel (SIMD) architectures. O n serial computers, these systems rely on Buchberger's algorithm t o compute Gr6bner bases. A pamllelixation of this algorithm is proposed, which addresses the potential growth in the number of polynomials that can be generated during the computation. The parallel algorithm was implemented on a Connection Machine CM-200 System. The experimental results which were obtained for seven test problems are examined, and the algorithm and its implementation are evaluated. The results of this study provide insights into ongoing research t o develop more eficient parallel algorithms for finding Grlibner bases. of algebra and geometry that must be solved computationally [7].B. Buchberger's work on Grobner bases [3, 41 inspired the development of algorithms to solve algebraic and geometric problems similar to those mentioned above. However, the actual computational complexity of these algorithms has hindered their use in largescale applications. For this reason, we have initiated a study to investigate the feasibility of computing Grobner bases on massively parallel architectures such as the MasPar or Connection Machine systems. The ability to do this would enable scientists to obtain solutions to a larger class of problems that contain a substantial number of polynomials and/or variables. Further, the introduction of parallelism could reduce the amount of computation time needed to obtain these solutions. This paper is a preliminary report that summarizes the current status of our study.
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