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Complexity Results for Bandwidth Minimization

M. R. Garey, R. L. Graham, D. S. Johnson and D. E. Knuth
SIAM Journal on Applied Mathematics
Vol. 34, No. 3 (May, 1978), pp. 477-495
Stable URL: http://www.jstor.org/stable/2100947
Page Count: 19
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Complexity Results for Bandwidth Minimization
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Abstract

We present a linear-time algorithm for sparse symmetric matrices which converts a matrix into pentadiagonal form ("bandwidth 2"), whenever it is possible to do so using simultaneous row and column permutations. On the other hand when an arbitrary integer k and graph G are given, we show that it is NP-complete to determine whether or not there exists an ordering of the vertices such that the adjacency matrix has bandwidth ≤ k, even when G is restricted to the class of free trees with all vertices of degree ≤ 3. Related problems for acyclic directed graphs (upper triangular matrices) are also discussed.

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