Geometric Spectral Partitioning

We investigate a new method for partitioning a graph into two equal-sized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applies to graphs that are meshes in Euclidean space). The new method does not require geometric coordinates, and it produces partitions that are often better than either the spectral or geometric ones.

[1]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[2]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[3]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[4]  A. George.  An automatic one-way dissection algorithm for irregular finite element problems , 1978 .

[5]  Charles E. Leiserson,et al.  Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[6]  D. Rose,et al.  A Separator Theorem for Chordal Graphs , 1982 .

[7]  John R Gilbert,et al.  A Separator Theorem for Graphs of Bounded Genus , 1984, J. Algorithms.

[8]  J. P. Blanks.  Near-optimal quadratic-based placement for a class of IC layout problems , 1985, IEEE Circuits and Devices Magazine.

[9]  Frank Thomson Leighton,et al.  An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[10]  J. Pach,et al.  An upper bound on the number of planar k-sets , 1989, 30th Annual Symposium on Foundations of Computer Science.

[11]  Robin Thomas,et al.  A separator theorem for graphs with an excluded minor and its applications , 1990, STOC '90.

[12]  Robert Schreiber,et al.  Solving unstructured grid problems on massively parallel computers , 1990 .

[13]  Roy D. Williams,et al.  Performance of dynamic load balancing algorithms for unstructured mesh calculations , 1991, Concurr. Pract. Exp..

[14]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[15]  Gary L. Miller,et al.  A unified geometric approach to graph separators , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[16]  Horst D. Simon,et al.  Partitioning of unstructured problems for parallel processing , 1991 .

[17]  Gary L. Miller,et al.  Automatic Mesh Partitioning , 1992 .

[18]  Bruce Hendrickson,et al.  The Chaco user`s guide. Version 1.0 , 1993 .

[19]  Charbel Farhat,et al.  Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics , 1993 .

[20]  S. Teng,et al.  A Cartesian Parallel Nested Dissection Algorithm , 1994 .

[21]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[22]  Shing-Tung Yau,et al.  A near optimal algorithm for edge separators (preliminary version) , 1994, STOC '94.

[23]  Tony F. Chan,et al.  A SIGN CUT VERSION OF THE RECURSIVE SPECTRAL BISECTION GRAPH PARTITIONING ALGORITHM , 1994 .

[24]  Gary L. Miller,et al.  Moments of Inertia and Graph Separators , 1994, SODA '94.

[25]  Gary L. Miller,et al.  Geometric mesh partitioning: implementation and experiments , 1995, Proceedings of 9th International Parallel Processing Symposium.

[26]  Gary L. Miller,et al.  On the performance of spectral graph partitioning methods , 1995, SODA '95.

[27]  Bruce Hendrickson,et al.  An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations , 1995, SIAM J. Sci. Comput..

[28]  Michael T. Heath,et al.  A Cartesian Parallel Nested Dissection Algorithm , 1992, SIAM J. Matrix Anal. Appl..