Approximating the bandwidth via volume respecting embeddings

Journal of Computer and System Sciences

Volumn 60, Issue 3, 2000, Pages 510-539

  Feige, Uriel ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONFORMAL MAPPING; GRAPH THEORY; LINEAR SYSTEMS; OPTIMAL SYSTEMS; RANDOM PROCESSES;

POLYLOGARITHMIC MULTIPLICATIVE FACTOR; RANDOMIZED ALGORITHM; SMALL DISTORTION EMBEDDINGS; VOLUME RESPECTING EMBEDDINGS;

BANDWIDTH;

EID: 0034206224     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1999.1682     Document Type: Article

References (32)

1. Assman S., Peck G., Syslo M., Zak J. The bandwidth of caterpillars with hairs of length 1 and 2. SIAM J. Algebraic Discrete Methods. 2:1981;387-393.
2. G. Blache, M. Karpinski, and, J. Wirtgen, On approximation intractability of the bandwidth problem, manuscript, 1998.
3. Blum A., Konjevod G., Ravi R., Vempala S. Semidefinite relaxations for minimum bandwidth and other vertex-ordering problems. Proc. of 30th STOC. 1998;. p. 100-105.
4. Bodlaender H., Fellows M., Hallet M. Beyond NP-completeness for problems of bounded width: hardness for the W hierarchy. Proc. of 26th STOC. 1994;. p. 449-458.
5. Bourgain J. On Lipschitz embedding of finite metric spaces in Hilbert space. Israel J. Math. 52:1985;46-52.
6. Chinn P., Chvatalova J., Dewdney A., Gibbs N. The bandwidth problem for graphs and matrices - a survey. J. Graph Theory. 6:1982;223-254.
7. Chung F., Seymour P. Graphs with small bandwidth and cutwidth. Discrete Math. 75:1989;113-119.
8. Chvatalova J. On the Bandwidth Problem for Graphs. 1980;University of Waterloo.
9. Cuthill E., McKee J. Reducing the bandwidth of sparse symmetric matrices. ACM National Conference Proc. 24:1969;157-172.
10. Frankl P., Maehara H. The Johnson-Lindenstrauss lemma and the sphericity of some graphs. J. Combin. Theory Ser. B. 44:1988;355-362.
11. Garey M., Graham R., Johnson D., Knuth D. Complexity results for bandwidth minimization. SIAM J. Appl. Math. 34:1978;477-495.
12. George A., Liu J. Computer Solution of Large Positive Definite Systems. 1981;Prentice-Hall.
13. Grotschel M., Lovasz L., Schrijver A. Geometric Algorithms and Combinatorial Optimization. 1987;Springer-Verlag, Berlin.
14. Gurari E., Sudborough I. Improved dynamic programming algorithms for bandwidth minimization and the min-cut linear arrangement problems. J. Algorithms. 5:1984;531-546.
15. Haralambides J., Makedon F., Monien B. Bandwidth minimization: an approximation algorithm for caterpillars. Math Systems Theory. 24:1991;169-177.
16. M. Karpinski, J. Wirtgen, and, A. Zelikovsky, An Approximation Algorithm for the Bandwidth Problem on Dense Graphs, ECCC TR97-017.
17. Kleitman D., Vohra R. Computing the bandwidth of interval graphs. SIAM J. Discrete Math. 3:1990;373-375.
18. Kloks T., Kratsch D., Muller H. Approximating the bandwidth for asteroidal triple-free graphs. Spirakis P. Algorithms - ESA '95. Lecture Notes in Computer Science. 979:1995;434-447 Springer-Verlag, Berlin.
19. Knuth D. The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. 1981;Addison-Wesley, Reading.
20. Gruber P. M., Lekkerkerker C. G. Geometry of Numbers. 1987;North Holland, Amsterdam.
21. Lagarias J. Point lattices. Graham R., Grotschel M., Lovasz L. Handbook of Combinatorics. 1995;MIT Press, Cambridge.
22. Linial N., London E., Rabinovich Y. The geometry of graphs and some of its algorithmic applications. Combinatorica. 15:1995;215-245.
23. Milman V., Schechtman G. Asymptotic Theory of Finite Dimensional Normed Spaces. Lecture Notes in Mathematics. 1200:1986;Springer-Verlag, Berlin.
24. Monien B. The bandwidth-minimization problem for caterpillars with hairlength 3 is NP-complete. SIAM J. Algebraic Discrete Methods. 7:1986;505-512.
25. Papadimitriou C. The NP-completeness of the bandwidth minimization problem. Computing. 16:1976;263-270.
26. Rao S. Small distortion and volume preserving embeddings for Planar and Euclidean metrics. Proc. of 15th Annual ACM Symposium on Computational Geometry. 1999;Miami Beach.
27. Santalo L. A. Integral geometry and geometric probability. Encyclopedia of Mathematics and its Applications. 1976;Addison-Wesley, Reading.
28. Saxe J. Dynamic programming algorithms for recognizing small-bandwidth graphs in polynomial time. SIAM J. Algebraic Methods. 1:1980;363-369.
29. Strang G. Linear Algebra and its Applications. 1988;Saunders.
30. Turner J. On the probable performance of heuristics for bandwidth minimization. SIAM J. Comput. 15:1986;561-580.
31. Unger W. The complexity of the approximation of the bandwidth problem. Proc. 39th Annual IEEE Symposium on Foundations of Computer Science. 1998;. p. 82-91.
32. Vempala S. Random projection: a new approach to VLSI layout. Proc. 39th Annual IEEE Symposium on Foundations of Computer Science. 1998;. p. 389-395.