Browsing by Subject "Hypergraph."

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Open Access
A constructive multi-way circuit partitioning algorithm based on minimum degree ordering
(1994) Çatalyürek, Ümit V
Circuit partitioning has many important applications in VLSI. Circuit partitioning problem can be most properly modeled as hypergraph partitioning. In this work, we propose a novel k-v/ay hypergraph partitioning heuristic using the Minimum Degree (MD) ordering which is a well-known heuristic for reducing the amount of fills in the factorization of symmetric sparse matrices. The proposed algorithm operates on the dual graph of the given hypergraph. The algorithm grows node-clusters on the dual graph which induce cell-clusters with locally minimum net-cut sizes. The quotient graph concept, widely used in MD ordering, is exploited for the sake of efficient implementation. The proposed algorithm outperforms well-known heuristics, such as Kernighan-Lin (KL) based algorithms and Simulated Annealing, in terms of solution quality on various VLSI benchmark circuits. A nice property of the proposed algorithm is that its execution time reduces with increasing k as opposed to the existing iterative heuristics. It is even faster than the fast KL-based algorithms on the partitioning of the benchmark circuits for k > 16.
Open Access
Partitioning sparse rectangular matrices for parallel computing of AAtX
(1999-09) Uçar, Bora
Many scientific applications involve repeated sparse matrix-vector and matrixtranspose-vector product computations. Graph and hypergraph partitioning based approaches used in the literature aim at minimizing the total communication volume while maintaining computational load balance through one dimensional partitioning of sparse matrices. In this thesis, we consider two approaches which consider minimizing both the total message count and communication volume while maintaining balance on the communication loads of the processors. Two communication schemes are investigated for the fold and expand operations needed in the parallel algorithm. For the global communication scheme, we show that the problem of minimizing concurrent communication volume can be formulated as the problem of permuting the sparse matrix into a singly-bordered block-diagonal form, where the total and concurrent message count is determined by the interconnection topology. For the personalized communication scheme, a two stage approach is proposed. In the first stage, the total communication volume is minimized while maintaining balance on the computational loads of the processors. In the second stage, a novel communication hypergraph model is proposed which enables the minimization of the total message count while maintaining balance on the communication loads of the processors through hypergraph-partitioning-like methods. The solution methods are tested on various matrices and results, which are quite attractive in terms of solution quality and running times, are obtained.
Open Access
Polyhedral Approaches to Hypergraph Partitioning and Cell Formation
(1994) Kandiller, Levent
Hypergraphs are generalizations of graphs in the sense that each hyperedge can connect more than two vertices. Hypergraphs are used to describe manufacturing environments and electrical circuits. Hypergraph partitioning in manufacturing models cell formation in Cellular Manufacturing systems. Moreover, hypergraph partitioning in VTSI design case is necessary to simplify the layout problem. There are various heuristic techniques for obtaining non-optimal hypergraph partitionings reported in the literature. In this dissertation research, optimal seeking hypergraph partitioning approaches are attacked from polyhedral combinatorics viewpoint. There are two polytopes defined on r-uniform hypergraphs in which every hyperedge has exactly r end points, in order to analyze partitioning related problems. Their dimensions, valid inequality families, facet defining inequalities are investigated, and experimented via random test problems. Cell formation is the first stage in designing Cellular Manufacturing systems. There are two new cell formation techniques based on combinatorial optimization principles. One uses graph approximation, creation of a flow equivalent tree by successively solving maximum flow problems and a search routine. The other uses the polynomially solvable special case of the one of the previously discussed polytopes. These new techniques are compared to six well-known cell formation algorithms in terms of different efficiency measures according to randomly generated problems. The results are analyzed statistically.