Bandwidth Minimization: An approximation algorithm for caterpillars
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
The Bandwidth Minimization Problem (BMP) is the problem, given a graphG and an integerk, to map the vertices ofG to distinct positive integers, so that no edge ofG has its endpoints mapped to integers that differ by more thank. There is no known approximation algorithm for this problem, even for the case of trees. We present an approximation algorithm for the BMP for the case of special graphs, called caterpillars. The BMP arises from many different engineering applications which try to achieve efficient storage and processing and has been studied extensively, especially with relation to other graph layout problems. In particular, the BMP for caterpillars is related to multiprocessor scheduling. It has been shown to be NP-complete, even for degree-3 trees. Our algorithm, gives a logn times optimal algorithm, wheren is the number of nodes of the caterpillar. It is based on the idea of level algorithms.
- C. H. Papadimitriou, The NP-completeness of the bandwidth minimization problem,Computing,16 (1976), 263–270.
- M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979.
- M. R. Garey, R. L. Graham, D. S. Johnson, and D. E. Knuth, Complexity results for bandwidth minimization,SIAM J. Appl. Math.,34 (1978), 477–495.
- J. B. Saxe, Dynamic programming algorithms for recognizing small bandwidth graphs in polynomial time,SIAM J. Algebraic Discrete Methods (1980).
- E. M. Gurari and I. H. Sudborough, Improved dynamic programming algorithms for bandwidth minimization and the min-cut linear arrangement problems,J. Algorithms,5 (1984), 531–546.
- B. Monien, The Bandwidth-Minimization Problem for Caterpillars with Hairlength 3 is NP Complete,SIAM J. Algebraic Discrete Methods,7 (1986), 505–512.
- S. F. Assman, G. W. Peck, M. M. Syslo, and J. Zak, The bandwidth of caterpillars with hairs of length 1 and 2,SIAM J. Algebraic Discrete Methods (1981), 387–391.
- J. Turner, Bandwidth and Probabilistic Complexity, Thesis, Northwestern University, Evanston, IL.
- E. Cuthill and J. McKee, Reducing the bandwidth of sparse symmetric matrices,ACM National Conference Proc.,24 (1969), 137–172.
- K. Y. Cheng, Minimizing the bandwidth of sparse symmetric matrices,Computing,11 (1973), 103–110.
- P. Z. Chinn, J. Chvatalova, A. K. Dewdney, and N. E. Gibbs, The bandwidth problem for graphs and matrices—a survey,J. Graph Theory,6 (1982), 223–254.
- I. Arany, L. Szoda, and W. F. Smith, An improved method for reducing the bandwidth of sparse symmetric matrices,Proc. 1971 IFIP Congress, pp. 1246–1250.
- F. R. K. Chung, Some problems and results in labeling of graphs, inThe Theory and Applications of Graphs (G. Chartrand, ed.), Wiley, New York, 1981, pp. 255–263.
- W. Lin and A. B. Sherman, Comparative analysis of the Cuthill-McKee ordering algorithms for sparse matrices,SIAM J. Numer. Anal.,13 (1976), 198–213.
- I. H. Sudborough, Bandwidth constraints on problems complete for polynomial time,Theoret. Comput. Sci.,26 (1983), 25–52.
- F. S. Makedon, Graph Layout Problems and Their Complexity, Ph.D. Thesis, August 1982, Electrical Engineering and Computer Science Department, Northwestern University, Evanston, IL.
- F. S. Makedon and I. H. Sudborough, Graph layout problems, inSurveys in Computer Science, (H. Maurer, ed.), Bibliographisches Institut, Zurich, 1984, pp. 145–192.
- M. M. Syslo and J. Zak, The Bandwidth Problem for Ordered Caterpillars, Report CS-80-065, Computer Science Department, Washington State University, 1980.
- Bandwidth Minimization: An approximation algorithm for caterpillars
Mathematical systems theory
Volume 24, Issue 1 , pp 169-177
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors
- Author Affiliations
- 1. Computer Science Program, The University of Texas at Dallas, MS MP 3.1, 75083-0688, Richardson, TX, USA
- 2. Department of Mathematics and Computer Science, University of Paderborn, Warburger Strasse, 4790, Paderborn, Federal Republic of Germany