We consider the following problem: given a set of points in the plane, each with a weight, and capacities of the four quadrants, assign each point to one of the quadrants such that the total weight of points assigned to a quadrant does not exceed its capacity, and the total distance is minimized.
This problem is most important in placement of VLSI circuits and is likely to have other applications. It is NP-hard, but the fractional relaxation always has an optimal solution which is “almost” integral. Hence for large instances, it suffices to solve the fractional relaxation. The main result of this paper is a linear-time algorithm for this relaxation. It is based on a structure theorem describing optimal solutions by so-called “American maps” and makes sophisticated use of binary search techniques and weighted median computations.
This algorithm is a main subroutine of a VLSI placement tool that is used for the design of many of the most complex chips. 相似文献
A method for the determination of trace impurities (U, Th, Ca, Fe, Cr, Ni, Cu, and Cd) in the refractory metals molybdenum and tungsten with isotope dilution mass Spectrometry (IDMS) has been developed. This method enables determinations of uranium and thorium down to the lowest pg/g level with high precision and accuracy. Selective chromatographic, extractive and electrolytic methods for the trace-matrix separation were combined with positive thermal ionization mass spectrometry. Different samples of high purity (4N) and of ultra high purity (UHP) materials for advanced technologies were analysed. The detection limits reached are (in ng/g): U 0.006, Th 0.008, Ca 10, Fe 19, Cr 0.5, Ni 0.6, Cu 2.7, and Cd 0.12. A comparison of results with other sensitive analytical methods (ICP-MS, GDMS, SIMS) makes obvious the urgent necessity of a reliable calibration method like IDMS because the analytical results obtained by the other methods often spread over a wide range. 相似文献
In this paper, we present the parallelization of tabu search on a network of workstations using PVM. Two parallelization strategies are integrated: functional decomposition strategy and multi-search threads strategy. In addition, domain decomposition strategy is implemented probabilistically. The performance of each strategy is observed and analyzed. The goal of parallelization is to speedup the search in finding better quality solutions. Observations support that both parallelization strategies are beneficial, with functional decomposition producing slightly better results. Experiments were conducted for the VLSI cell placement, an NP-hard problem, and the objective was to achieve the best possible solution in terms of interconnection length, timing performance (circuit speed), and area. The multiobjective nature of this problem is addressed using a fuzzy goal-based cost computation. 相似文献