Abstract
We present approximation algorithms for the Bandwidth Minimization Problem (BMP) for cases of special trees. The BMP has many different applications and has been studied for both graphs and matrices. The problem has important applications in large distributed processing systems and databases as well as communication theory. The technique presented here is used to provide a communication protocol for maximum throughput and concurrency control. We study the problem on a tree network model having the following property: For any node of the tree, if more than one subtree is present, then the difference of the depths of the subtrees is bounded. We call these trees special height balanced trees. If this difference is a constant on the size of the depth d of the tree, then an O(log d) algorithm is presented. For any depth difference F(d), where F(d)≪d, the approximation factor becomes O(F(d)log d).
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References
C.H. Papadimitriou, "The NP-completeness of the Bandwidth Minimization Problem", Computing, 16 (1976) pp. 263–270.
M.R. Garey, D.S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-completeness", W.H. Freeman and Company, 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), pp. 477–495.
J.B. Saxe, "Dynamic Programming Algorithms for Recognizing Small Bandwidth Graphs in Polynomial Time", SIAM J. on Algebraic and Discrete Methods, December, 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), pp. 531–546.
E. Cuthill, J. McKee, "Reducing the Bandwidth of Sparse Symmetric Matrices", ACM National Conference Proc. 24, (1969), pp. 137–172.
K.Y. Cheng, "Minimizing the Bandwidth of Sparse Symmetric Matrices", Computing 11, (1973), pp. 103–110.
P.Z. Chinn, J. Chvatalova, A.K. Dewdney, N.E. Gibbs, "The Bandwidth Problem for Graphs and Matrices-A Survey", J. of Graph Theory, Vol. 6, (1982), pp. 223–254.
J. Haralambides, F. Makedon and B. Monien, "Bandwidth Minimization: An Approximation Algorithm for Caterpillars", J. of Mathematical Systems Theory, to appear.
J. Haralambides, F. Makedon and B. Monien, "Approximation Algorithms for the Bandwidth Minimization Problem for Caterpillar Graphs", Proc. of the 2nd Symposium of Parallel and Distributed Processing, 1990, pp. 301–307.
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© 1991 Springer-Verlag Berlin Heidelberg
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Haralambides, J., Makedon, F. (1991). Approximation algorithms for the Bandwidth Minimization Problem for a large class of trees. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_155
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DOI: https://doi.org/10.1007/3-540-54029-6_155
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