On Spectral Bounds for the k-Partitioning of Graphs

Theory of Computing Systems

Volumn 36, Issue 5, 2003, Pages 461-478

  Elsässer, Robert ^a   Lücking, Thomas ^a   Monien, Burkhard ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

INTERPROCESSOR COMMUNICATION;

BOUNDARY CONDITIONS; COMMUNICATION SYSTEMS; MULTIPROCESSING SYSTEMS; PARALLEL PROCESSING SYSTEMS; SPECTRUM ANALYSIS;

GRAPH THEORY;

EID: 0142228761     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-003-1083-9     Document Type: Conference Paper

References (23)

1. S. Bezrukov. On k-partitioning the n-cube. In Proc. 22nd International Workshop, WG 1996, LNCS 1197, pages 44-55, 1996.
2. S. Bezrukov, R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich. New spectral lower bounds on the bisection width of graphs. In Proc. 26th International Workshop, WG 2000, LNCS 1928, pages 23-34, 2000.
3. S. Bezrukov and B. Rovan. On partitioning grids into equal parts. Comput. Artificial Intell., 16:153-165, 1997.
4. M. Bolla. Spectra, euclidean representations and clusterings of hypergraphs. Discrete Math., 117:19-40, 1993.
5. M. Bolla and G. Tusnády. Spectra and optimal partitions of weighted graphs. Discrete Math., 128:1-20, 1994.
6. T. Bui, S. Chaudhuri, F. Leighton, and M. Sisper. Graph bisection algorithms with good average case behaviour. Combinatorica, 7(2):171-191, 1987.
7. F. Chung and S.-T. Yao. A near optimal algorithm for edge separators. In Proc. 26th ACM Symp. on Theory of Computing, pages 1-8, 1994.
8. D. Cvetkovic, M. Doob, and H. Sachs. Spectra of Graphs, 3rd edn. Johann Ambrosius Barth, Heidelberg, 1995.
9. P. Davis. Circulant Matrices. Wiley, New York, 1979.
10. R. Diekmann, R. Lüling, B. Monien, and C. Spräner. Combining helpful sets and parallel simulated annealing for the graph-partitioning problem. Internat. J. Parallel Algorithms Appl., 8:61-84, 1996.
11. W. Donath and A. Hoffman. Lower bounds for the partitioning of graphs. IBM J. Res. Develop., 17:420-425, 1973.
12. J. Falkner, F. Rendl, and H. Wolkowicz. A computational study of graph partitioning. Math. Programming, 66:211-239, 1994.
13. M. Garey, D. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoret. Comput. Sci., 1:237-267, 1976.
14. J. Gilbert, G. Miller, and S.-H. Teng. Geometric mesh partitioning: implementation and experiments. In Proc. IPPS 1995, pages 418-427, 1995.
15. S. Guattery and G. Miller. On the performance of spectral graph partitioning methods. In Proc. Sixth Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 233-242, 1995.
16. S. Hadley, F. Rendl, and H. Wolkowicz. A new lower bound via projection for the quadratic assignment problem. Math. Oper. Res., 17:727-739, 1992.
17. A. Hoffman and H. Wielandt. The variation of the spectrum of a normal matrix. Duke Math. J., 20:37-39, 1953.
18. F. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.
19. A. Pothen, H. Simon, and K. Liu. Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl., 11(3):430-452, 1990.
20. F. Rendl and H. Wolkowicz. A projection technique for partitioning the nodes of a graph. Ann. Oper. Res., 58:155-179, 1995.
21. D. A. Spielman and S.-H. Teng. Spectral partitioning works: planar graphs and finite element meshes. In Proc. 31th Conf. on Foundations of Computer Science, pages 96-105, 1996.
22. J.-P. Tillich. The eigenvalues of the double-rooted tree. Manuscript, 1999.
23. J. H. Wilkinson. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, 1965.