Moments of inertia and graph separators

Journal of Combinatorial Optimization

Volumn 1, Issue 1, 1997, Pages 79-104

  Gremban, Keith D ^a   Miller, Gary L ^b   Teng, Shang Hua ^c  

^a Advanced Information Systems Division   (United States)

^b Carnegie Mellon University   (United States)

^c University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 25644444015     PISSN: 13826905     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009763020645     Document Type: Article

References (38)

1. Alon, N., P. Seymour, and R. Thomas. A separator theorem for non-planar graphs. In Proceedings of the 22th Annual ACM Symposium on Theory of Computing, Maryland, May 1990. ACM.
2. Blelloch, G., A. Feldmann, O. Ghattas, J. Gilbert, G. Miller, D. R. O'Hallaron, E. Schwabe and J. Schewchuk, S.-H. Teng. (1996). Automated parallel solution of unstructured PDE problems. CACM, invited submission, to appear.
3. Clarkson, K., D. Eppstein, G. L. Miller, C. Sturtivant, and S.-H. Teng. Approximating center point with iterated radon points. In Proceedings of 9th ACM Symposium on Computational Geometry, pp. 91-98, San Diego, May, 1993.
4. Crawford, G. E. Elementary proof that the arithmetic mean of any number of positive quantities is greater than the geometric mean. Proc. Edinburgh Math. Soc., 17:2-4, 1899-1900.
5. Djidjev, H. N. On the problem of partitioning planar graphs. SIAM J. Alg. Disc. Math., 3(2):229-240, June 1982.
6. Donath, W. E. (1988). Logic partitioning. In B. T. Preas and M. J. Lorenzetti, eds., Physical Design Automation of VLSI Systems, pp. 65-86. Benjamin/Cummings.
7. Donath, W. E., and A. J. Hoffman. (1972). Algorithms for partitioning of graphs and computer logic based on eigenvectors of connection matrices. IBM Technical Disclosure Bulletin, 15:938-944.
8. Eppstein, D., G. L. Miller, and S.-H. Teng. (1993). A deterministic linear time algorithm for geometric separators and its applications. In Proceedings of 9th ACM Symposium on Computational Geometry, pp. 99-108, San Diego, May.
9. Farhat, C., and M. Lesoinne. (1993). Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Int. J. Num. Meth. Eng. 36:745-764.
10. Farhat, C., and H. Simon. (1993). TOP/DOMDEC - a software tool for mesh partitioning and parallel processing. Technical Report, NASA Ames Research Center.
11. Frieze, A. M., G. L. Miller, and S.-H. Teng. (1992). Separator based parallel divide and conquer in computational geometry. In 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pp 420-430.
12. Gazit, H. (1986). An improved algorithm for separating a planar graph. Manuscript, Department of Computer Science, University of Southern California.
13. Gazit, H., and G. L. Miller. A parallel algorithm for finding a separator in planar graphs. In 28st Annual Symposium on Foundation of Computation Science, IEEE, 238-248, Los Angeles, October 1987.
14. George, J. A. (1973). Nested dissection of a regular finite element mesh. SIAM J. Numerical Analysis, 10:345-363.
15. George, A., and J. W. H. Liu. (1981). Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall.
16. Gilbert, J. R., J. P Hutchinson, and R. E. Tarjan. (1984). A separation theorem for graphs of bounded genus. J. Algorithms, 5:391-407.
17. Gilbert, J. R., G. L. Miller, and S.-H. Teng. (1995). Geometric mesh partitioning: Implementation and experiments. In International Conference of Parallel Processing, pp 418-427.
18. Heath, M., and P. Raghavan. (1994). A cartesian parallel nested dissection algorithm. To appear in SIAM Journal on Matrix Analysis and Applications.
19. Hendrickson, B., and R. Leland. (1993). Multidimensional spectral load balancing. Technical Report, Sandia National Laboratories, SAND93-0074.
20. Hendrickson, B., and R. Leland. (1993). A multilevel algorithm for partitioning graphs. Technical Report SAND93-1301, Sandia National Laboratories, Albuquerque, NM.
21. Hendrickson, B., and R. Leland. (1993). The Chaco user's guide, Version 1.0. Technical Report SAND93-2339, Sandia National Laboratories, Albuquerque, NM.
22. Jordan, C. (1869). Sur les assemblages de lignes. Journal Reine Angew. Math, 70:185-190.
23. Kernighan B. W., and S. Lin. (1970). An efficient heuristic procedure for partitioning graphs. Bell Sys. Tech. J., 49: 291-307.
24. Leighton, F. T. (1983). Complexity Issues in VLSI. Foundations of Computing. MIT Press, Cambridge, MA.
25. Leighton, F T., and S. Rao. (1988). An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. In 29th Annual Symposium on Foundations of Computer Science, pp 422-431.
26. Leiserson, C. E. (1983). Area Efficient VLSI Computation. Foundations of Computing. MIT Press, Cambridge, MA.
27. Lipton, R. J., D. J. Rose, and R. E. Tarjan. (1979). "Generalized nested dissection". SIAM J. on Numerical Analysis, 16:346-358.
28. Lipton, R. J., and R. E. Tarjan. (1979). "A separator theorem for planar graphs". SIAM J. of Appl. Math., 36(April), 177-189.
29. Miller, G. L. (1986). Finding small simple cycle separators for 2-connected planar graphs. Journal of Computer and System Sciences, 32(3)(June), 265-279.
30. Miller, G. L., S.-H. Teng, W. Thurston, and S. A. Vavasis. (1996). "Automatic Mesh Partitioning." In A. George, J. Gilbert, and J. Liu, editors, Sparse Matrix Computations: Graph Theory Issues and Algorithms, IMA Volumes in Mathematics and its Applications. Springer-Verlag.
31. Miller, G. L., S.-H. Teng, W. Thurston, and S. A. Vavasis. (1996). Finite element meshes and geometric separators. SIAM J. Scientific Computing, to appear.
32. Nour-Omid, B., A. Raefsky, and G. Lyzenga. (1987). Solving finite element equations on concurrent computers. in A. K. Noor, ed., Parallel Computations and Their Impact on Mechanics, The American Society of Mechanical Engineers, AMD-Vol. 86, 209-228.
33. Pan, V., and J. Reif. (1985). Efficient parallel solution of linear systems. In Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pages 143-152, Providence, RI, May. ACM.
34. Pothen, A., H. D. Simon, and K.-P. Liou. (1990). Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Mat. Anal. Appl., 11(3):430-452.
35. Simon, H. D. (1991). Partitioning of unstructured problems for parallel processing. Computing Systems in Engineering 2(2/3):135-148.
36. Teng, S.-H.. (1991). Points, Spheres, and Separators: a unified geometric approach to graph partitioning. Ph.D. Thesis, Carnegie Mellon University, CMU-CS-91-184.
37. Ungar, P. (1951). A theorem on planar graphs. Journal London Math Soc. 26:256-262.
38. Williams, R. D. (1991). Performance of dynamic load balancing algorithms for unstructured mesh calculations Concurrency: Practice and Experience, 3(5):457-481.