Bandwidth Minimization: An approximation algorithm for caterpillars
 J. Haralambides,
 F. Makedon,
 B. Monien
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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 NPcomplete, even for degree3 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.
 Papadimitriou, C. H. (1976) The NPcompleteness of the bandwidth minimization problem. Computing 16: pp. 263270
 Garey, M. R., Johnson, D. S. (1979) Computers and Intractability: A Guide to the Theory of NPcompleteness. Freeman, San Francisco
 Garey, M. R., Graham, R. L., Johnson, D. S., Knuth, D. E. (1978) Complexity results for bandwidth minimization. SIAM J. Appl. Math. 34: pp. 477495
 J. B. Saxe, Dynamic programming algorithms for recognizing small bandwidth graphs in polynomial time,SIAM J. Algebraic Discrete Methods (1980).
 Gurari, E. M., Sudborough, I. H. (1984) Improved dynamic programming algorithms for bandwidth minimization and the mincut linear arrangement problems. J. Algorithms 5: pp. 531546
 Monien, B. (1986) The BandwidthMinimization Problem for Caterpillars with Hairlength 3 is NP Complete. SIAM J. Algebraic Discrete Methods 7: pp. 505512
 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.
 Cuthill, E., McKee, J. (1969) Reducing the bandwidth of sparse symmetric matrices. ACM National Conference Proc. 24: pp. 137172
 Cheng, K. Y. (1973) Minimizing the bandwidth of sparse symmetric matrices. Computing 11: pp. 103110
 Chinn, P. Z., Chvatalova, J., Dewdney, A. K., Gibbs, N. E. (1982) The bandwidth problem for graphs and matrices—a survey. J. Graph Theory 6: pp. 223254
 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.
 Chung, F. R. K. Some problems and results in labeling of graphs. In: Chartrand, G. eds. (1981) The Theory and Applications of Graphs. Wiley, New York, pp. 255263
 Lin, W., Sherman, A. B. (1976) Comparative analysis of the CuthillMcKee ordering algorithms for sparse matrices. SIAM J. Numer. Anal. 13: pp. 198213
 Sudborough, I. H. (1983) Bandwidth constraints on problems complete for polynomial time. Theoret. Comput. Sci. 26: pp. 2552
 F. S. Makedon, Graph Layout Problems and Their Complexity, Ph.D. Thesis, August 1982, Electrical Engineering and Computer Science Department, Northwestern University, Evanston, IL.
 Makedon, F. S., Sudborough, I. H. Graph layout problems. In: Maurer, H. eds. (1984) Surveys in Computer Science. Bibliographisches Institut, Zurich, pp. 145192
 M. M. Syslo and J. Zak, The Bandwidth Problem for Ordered Caterpillars, Report CS80065, Computer Science Department, Washington State University, 1980.
 Title
 Bandwidth Minimization: An approximation algorithm for caterpillars
 Journal

Mathematical systems theory
Volume 24, Issue 1 , pp 169177
 Cover Date
 19911201
 DOI
 10.1007/BF02090396
 Print ISSN
 00255661
 Online ISSN
 14330490
 Publisher
 SpringerVerlag
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 Authors

 J. Haralambides ^{(1)}
 F. Makedon ^{(1)}
 B. Monien ^{(2)}
 Author Affiliations

 1. Computer Science Program, The University of Texas at Dallas, MS MP 3.1, 750830688, Richardson, TX, USA
 2. Department of Mathematics and Computer Science, University of Paderborn, Warburger Strasse, 4790, Paderborn, Federal Republic of Germany