The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
An $0(n \log n)$ Algorithm for Bandwidth of Interval Graphs
SIAM Journal on Discrete Mathematics
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Improved bandwidth approximation for trees and chordal graphs
Journal of Algorithms
A survey of graph layout problems
ACM Computing Surveys (CSUR)
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
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Graph bandwidth minimization (GBM) is a classical and challenging problem in graph algorithms and combinatorial optimization. Most of existing researches on this problem have focused on unweighted graphs. In this paper, we study the bandwidth minimization problem of weighted caterpillars, and propose several algorithms for solving various types of caterpillars. More specifically, we show that the GBM problem of caterpillars with hair-length at most 2 and the GBM problem of star-shape caterpillars are NP-complete, and give a lower bound of the graph bandwidth for general weighted graphs. For caterpillars with hair-length at most 1, we present an O(n log n log (nwmax))-time algorithm to compute an optimal bandwidth layout, where n is the total number of vertices in the graph and wmax is the maximum edge weight. For caterpillars with hair-length at most k, we give a k-approximation algorithm. For arbitrary caterpillars and general graphs, we give a heuristic algorithm. Experiments show that the solutions obtained by our heuristic algorithm are roughly within a factor of log (2n) of the lower bound.