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Techniques on some hypergraphs that are part of widely used acm sigda [19] circuit partitioning benchmarks suite. the characteristics of these hypergraphs are shown in table 1. the proposed method is implemented in `c' programming language on a sun ultra10 workstation. the comparison is based on good initial solutions obtained by each heuristic and the computation time involved to obtain these solutions. tables 2 and 3 present results based on random initial solutions, barnes's eigenvector algorithm, grasp, genetic algorithm and the memetic algorithm. these tables basically introduce the initial cuts for several benchmarks obtained by the constructive based techniques for two and four blocks respectively. the cpu time for the partitions obtained by the barnes's algorithm include the time for forming the graph adjacency matrix, finding the eigenvalues and eigenvectors. it is interesting to note that most solutions obtained by the grasp, genetic algorithm and memetic algorithm are superior to those obtained by the eigenvector approach. the computation time used by the grasp is the least compared to the three other methods. the last row in the table presents the improvement of solution quality using all methods with respect to the solutions obtained randomly. on average the barnes numerical method reduces the amounts of cuts by 81% for two way partitioning and 65% for four way partitioning. the performance of grasp, ga, and the memetic algorithm is better than that of barnes numerical techniques. also, eigenvector techniques can be slow to converge, whereas grasp, ga's are more stable and give superior results. tables 4 and 5 introduce the results after applying the fiduccia and mattheyses fm ; local interchange heuristic. it is interesting to notice that while barnes eigen vector technique ; gives a modest reduction in cut-size of about 5-9% over the random approach, the reduction of computation time is noticeable. among the other three techniques grasp seems to offer the best approach for two-way partitioning, but the memetic algorithm outperforms grasp as the number of partitions increase on the expense of computation time.
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Summary of the invention in accordance with the preferred embodiment of the present invention, there is provided a collapsible, portable casino craps table.
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Statement of statewide policy objectives: this rulemaking does not create or expand any state mandates on units of local government. time, place and manner in which interested persons may comment on this proposed rulemaking: interested persons may present their comments concerning this rulemaking within 45 days after the publication of this issue of the illinois register to: susan meister division of legal services illinois department of public health 535 w. jefferson st., 5th floor springfield, illinois 62761 217 782-2043 e-mail: rules idph ate.il.
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