Spectral methods for graph bisection problems

Computers and Operations Research

Volumn 25, Issue 7-8, 1998, Pages 519-530

  Tu, Chih Chien ^a   Cheng, Hsuanjen ^b  

^a POLYTECHNIC UNIVERSITY   (United States)

^b NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Eigenvalue; Eigenvector; Interior point method; Semidefinite programming; Subgradient method

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL PROGRAMMING; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PROBLEM SOLVING;

INTERIOR POINT METHOD; SEMIDEFINITE PROGRAMMING; SUBGRADIENT METHOD;

GRAPH THEORY;

EID: 0032120702     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(98)00021-5     Document Type: Article

References (27)

1. Alizadeh, F., Haeberly, J. A. and Overton, M. L., A new primal-dual interior-point method for semidefinite programming. Technical Report 659. Computer Science Department, Courant Institute of Mathematical Sciences, New York University, U.S.A., 1994.
2. Barnes, E. R., An algorithm for partitioning the nodes of a graph. SIAM Journal on Algebraic and Discrete Methods, 1982, 3, 541-550.
3. Bui, T. N., Leighton, F. T. and Heigham, C., Improving the performance of the kernighan-lin and simulated annealing graph bisection algorithms. Proceedings 26th IEEE Design Automation Conference. U.S.A., 1989, pp. 775-778.
4. Barnes, E. R. and Hoffman, A. J., Partitioning, Spectra and Linear Programming. Academic Press, U.S.A., 1984.
5. Boppana, R. B., Eigenvalues and graph bisection: An average case analysis. Proceedings of the 28th Annual Symposium on Computer Science, IEEE, 1987, pp. 280-285.
6. Bui, T. N., Leighton, F. T., Chaudhuri, S. and Sipser, M., Graph bisection algorithms with good average case behavior. Combinatorica, 1987, 7, 171-191.
7. Barnes, E. R., Vannelli, A. and Walker, J. Q., A new heuristic for partitioning the nodes of a graph. SIAM Journal on Discrete Mathematics, 1988, 3, 299-305.
8. Christofides, N. and Brooker, P., The optimal partitioning of graphs. SIAM Journal on Applied Mathematics, 1976, 30, 55-69.
9. Cullum, J. and Donath, W. E., A block Lanczos algorithm for computing the q algebraically largest eigenvalues and corresponding eigenspace of large, sparse, real symmetric matrices. Proceedings of the 1974 IEEE Conference on Decision and Control. 1974, pp. 505-509.
10. Cullum, J., Donath, W. E. and Wolfe, P., The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices. Mathematical Programming Study, 1975, 3, 35-55.
11. Donath, W. E. and Hoffman, A. J., Lower bound for the partitioning of graphs. IBM Journal of Research and Development, 1973, 17, 420-425.
12. Falkner, J., Rendl, F. and Wolkowicz, H., A computational study of graph partitioning. Technical Report CORR-92-25. University of Waterloo, 1993.
13. Garey, M. R., Johnson, D. S. and Stockmeyer, L., Some simplified NP-complete graph problems. Theoretical Computer Science, 1976, 1, 237-267.
14. Goldberg, M. and Miller, Z., A parallel algorithm for bisection width in trees. Technical report, 1986.
15. Helmberg, C., Rendl, F., Vanderbei, R. and Wolkowicz, H., An interior-point method for semidefinite programming. Program in statistics and operations research, Princeton University. SIAM Journal on Optimization, 1996, 6, 342-361.
16. Kernighan, B. W. and Lin, S., An efficient heuristic procedure for partitioning graphs. Bell Systems Technol. J., 1970, 49, 291-307.
17. Kojima, M., Mizuno, S. and Yoshise, A., A Primitive Interior Point Algorithm for Semidefinite Programs in Mathematica. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan, 1994.
18. Lengauer, T., Combinatorial Algorithms for Integrated Circuit Layout. John Wiley and Sons, Chicester, 1990.
19. Lustig, I. J., Marsten, R. E. and Shanno, D. F., On implementing mehrota's predictor-corrector interior point method for linear programming. SIAM Journal on Optimization, 1992, 2, 435-449.
20. Mohar, B. and Poljak, S., Eigenvalues in combinatorial optimization. IMA Vol. Math. Appl., 1993, 50, 107-151.
21. Overton, M. L., On minimizing the maximum eigenvalue of a symmetric matrix. SIAM Journal on Matrix Analysis and Applications, 1988, 9, 256-268.
22. Overton, M. L., Large-scale optimization of eigenvalues. SIAM Journal on Optimization, 1992, 2, 88-120.
23. Poljak, S. and Rendl, F., Nonpolyhedral relaxations of graph-bisection problems. SIAM Journal on Optimization, 1995, 5, 467-487.
24. Papadimitriou, C. H. and Sideri, M., The bisection width of grid graphs. Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 405-410.
25. Rendl, F. and Wolkowicz, H., A projection technique for partitioning the nodes of a graph. Technical Report 20, University of Waterloo, 1990.
26. Schramm, H. and Zowe, J., A combination of the bundle approach and the trust region concept. Advances in Mathematical Optimization, Vol. 45. Math. Res., Akademie-Verlag, Berlin, 1988, pp. 196-209.
27. Vandenberghe, L. and Boyd, S., Semidefinite programming. SIAM Review, 1996, 38, 49-95.