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- W2117611406 abstract "This thesis presents new approaches to multi-way partitioning of graphs and hypergaphs. Our primary application is VLSI circuit design, where the need for fast and effective methods has dramatically increased in step with the complexity and design methodology requirements for high-end systems.Our first set of approaches explores the problem of dividing a given vertex ordering into a multi-way partitioning. We show that dynamic programming can find the optimal solution to this restricted partitioning formulation for a variety of partitioning objectives and constraints. As a result, multi-way partitioning reduces to the problem of finding a good vertex ordering. This technique can be applied to data classification, circuit clustering, and circuit partitioning; we present vertex ordering constructions specific to each of these applications.Next, we explore spectral graph partitioning approaches which construct a solution from the eigenvectors and eigenvalues of a matrix representation of the graph. We map each vertex of the graph to a vector in a multi-dimensional space; these vectors define an instance of what we call the vector partitioning problem. Our main result establishes the equivalence of vector partitioning and graph partitioning: the set of vectors is an exact geometric representation of the original graph, enabling us to apply vector partitioning heuristics to obtain graph partitioning solutions.Finally, we propose a new multilevel partitioning algorithm that utilizes the latest innovations in iterative partitioning heuristics. Our approach yields state-of-the-art results for both 2-way and 4-way partitioning." @default.
- W2117611406 created "2016-06-24" @default.
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- W2117611406 date "1996-01-01" @default.
- W2117611406 modified "2023-10-16" @default.
- W2117611406 title "Multi-way graph and hypergraph partitioning" @default.
- W2117611406 hasPublicationYear "1996" @default.
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