This article presents a new method for finding initial partitioning for fiduccia-mattheyses algorithm that makes it possible to work out a qualitative approximate solution for the original balanced hypergraph partitio...
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This article presents a new method for finding initial partitioning for fiduccia-mattheyses algorithm that makes it possible to work out a qualitative approximate solution for the original balanced hypergraph partitioning problem. The proposed method uses geometrical properties and dimension reduction methods for metric spaces of large dimensions.
Iterative improvement partitioning algorithms such as the FM algorithm of fiduccia and mattheyses [8], the algorithm of Krishnamurthy [13], and Sanchis's extensions of these algorithms to multiway partitioning [16...
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Iterative improvement partitioning algorithms such as the FM algorithm of fiduccia and mattheyses [8], the algorithm of Krishnamurthy [13], and Sanchis's extensions of these algorithms to multiway partitioning [16] all rely on efficient data structures to select the modules to be moved from one partition to the other, The implementation choices for one of these data structures, the gain bucket, is investigated, Surprisingly, selection from gain buckets maintained as last-in-first-out (LIFO) stacks leads to significantly better results than gain buckets maintained randomly (as in previous studies of the FM algorithm [13], [16]) or as first-in-first-out (FIFO) queues. In particular, LIFO buckets result in a 36% improvement over random buckets and a 43% improvement over FIFO buckets for minimum-cut bisection, Eliminating randomization from the bucket selection not only improves the solution quality, but has a greater impact on FM performance than adding the Krishnamurthy gain vector. The LIFO selection scheme also results in improvement over random schemes for multiway partitioning [16] and for more sophisticated partitioning strategies such as the two-phase FM methodology [2], Finally, by combining insights from the LIFO gain buckets with the Krishnamurthy higher-level gain formulation, a new higher-level gain formulation is proposed, This alternative formulation results in a further 22% reduction in the average cut cost when compared directly to the Krishnamurthy formulation for higher-level gains, assuming LIFO organization for the gain buckets.
In the spectral method, the vertices in a graph can be mapped into the vectors in d-dimensional space, thus the vectors are partitioned instead of vertices to obtain graph partitioning. In this paper, we show a method...
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ISBN:
(纸本)9780818677861
In the spectral method, the vertices in a graph can be mapped into the vectors in d-dimensional space, thus the vectors are partitioned instead of vertices to obtain graph partitioning. In this paper, we show a method to obtain optimal two-way vector partitioning based on an optimal direction vector. As the problem to find the optimal direction vector is NP-problem, we propose an efficient heuristic to obtain high quality direction vector. As we approximate a given netlist into the graph and only use ten eigenvectors in practice, there is a chance to improve the solution quality by local optimization. fiduccia-mattheyses algorithm is employed as a post processing. Compared with FM and MELO, the proposed algorithm PDV reduces cutsize on the average 40% and 20.5%, respectively.
The graph bisection problem is to partition a given graph into two subgraphs with equal size with minimizing the cutsize. This problem is NP-hard, and hence several heuristic algorithms have been proposed. Among them,...
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The graph bisection problem is to partition a given graph into two subgraphs with equal size with minimizing the cutsize. This problem is NP-hard, and hence several heuristic algorithms have been proposed. Among them, the Kernighan-Lin algorithm and the fiduccia-mattheyses algorithm are well known, and widely used in practical applications. Since those algorithms are iterative improvement algorithms, in which the current solution is iteratively improved by interchanging a pair of two nodes belonging to different subgraphs, or moving one node from one subgraph to the other, those algorithms tend to fall into a local optimum. In this paper, we present a heuristic algorithm based on subgraph migration to avoid falling into a local optimum. In this algorithm, an initial solution is given, and it is improved by moving a subgraph, which is effective to reduce the cutsize. The algorithm repeats this operation until no further improvement can be achieved. Finally, the balance of the bisection is restored by moving nodes to get a final solution. Experimental results show that the proposed algorithm gets better solutions than the Kernighan-Lin and fiduccia-mattheyses algorithms.
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