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Abstract: We discuss algorithms for graph bisection which are relevant to the distribution of tasks, such as the elements and nodes of an unstructured mesh to the processors of a parallel computer. Starting with a cost function consisting of a part to ensure equal numbers of tasks for each processor, and a part to minimize communication time between processors, we derive the spectral bisection method, which consists of finding an eigenvector of a large sparse matrix. Inertial bisection is derived as a... (Update)
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.... the computation load has to be balanced among the different processors and the amount of communication has to be minimized [53, 24, 55, 60, 32, 26]. The bisection problem is of great relevance in VLSI design because it models the problem of optimally placing standard cells...
...the process continues recursively until p partitions are generated. A more elaborated geometric approach is inertial method [7, 14]. It employs a physical analogy in which the grid points are treated as point masses and the grid is cut with a plane orthogonal to the...
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BibTeX entry: (Update)
R. Williams, "Unification of Spectral and Inertial Bisection," Techn. Rep., Caltech, 1994. Available at: http://www.cacr.caltech.edu/roy/papers/ GREEDY, PROHIBITION, AND REACTIVE HEURISTICS FOR GRAPH PARTITIONING 36 http://citeseer.ist.psu.edu/williams94unification.html More
@techreport{ williams94unification,
author = "Roy Williams",
title = "Unification of Spectral and Inertial Bisection",
number = "CCSF-48",
year = "1994",
url = "citeseer.ist.psu.edu/williams94unification.html" }
Citations (may not include all citations):309 Partitioning Sparse Matrices with Eigenvectors of Graphs (context) - Pothen, Simon et al. - 1990
209 Computer Science Press (context) - Even, Algorithms - 1979
144 Performance of Dynamic Load Balancing Algorithms for Unstruc.. - Williams - 1991
108 Algebraic Connectivity of Graphs (context) - Fiedler - 1973
92 A Property of Eigenvectors of Non-negative Symmetric Matrice.. (context) - Fiedler - 1975
88 Eigenvalues and Graph Bisection: an Average Case Analysis (context) - Boppana - 1987
11 Fast Mapping and Remapping Algorithm for Irregular and Adapt.. - Ou, Ranka et al.
3 A Fast Implementation of Recursive Spectral Bisection for Pa.. (context) - Barnard, Simon - 1993
http://www.nas.nasa.gov/RNR/People/hsimon/RNR-93-012/RNR-93-012.ps
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