Journal ArticleDOI
The bandwidth problem for graphs and matrices—a survey
TLDR
This survey describes all the results known to the authors as of approximately August 1981 and describes the effect on bandwidth of local operations such as refinement and contraction of graphs, bounds on bandwidth in terms of other graph invariants, the bandwidth of special classes of graph, and approximate bandwidth algorithms for graphs and matrices.Abstract:
The bandwidth problem for a graph G is to label its n vertices vi with distinct integers f(vi) so that the quantity max{| f(vi) − f(vi)| : (vi vj) ∈ E(G)} is minimized. The corresponding problem for a real symmetric matrix M is to find a symmetric permutation M' of M so that the quantity max{| i − j| : m'ij ≠ 0} is minimized. This survey describes all the results known to the authors as of approximately August 1981. These results include the effect on bandwidth of local operations such as refinement and contraction of graphs, bounds on bandwidth in terms of other graph invariants, the bandwidth of special classes of graphs, and approximate bandwidth algorithms for graphs and matrices. The survey concludes with a brief discussion of some problems related to bandwidth.read more
Citations
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The Algorithm Design Manual
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A survey of graph layout problems
TL;DR: A complete view of the current state of the art with respect to layout problems from an algorithmic point of view is presented.
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The network inhibition problem
TL;DR: The Network Inhibition Problem as discussed by the authors ) is a classic example of network inhibition problem and it is NP-hard to find solutions to it, e.g., as discussed by the authors.
Journal ArticleDOI
Approximating the Bandwidth via Volume Respecting Embeddings
TL;DR: A randomized algorithm that runs in nearly linear time and outputs a linear arrangement whose bandwidth is within a polylogarithmic multiplicative factor of optimal, based on a new notion, called volume respecting embeddings.
Book ChapterDOI
Graph Layout Problems Parameterized by Vertex Cover
TL;DR: This paper study's basic ingredient is a classical algorithm for Integer Linear Programming when parameterized by dimension, designed by Lenstra and later improved by Kannan, showing that all the mentioned problems are fixed parameter tractable.
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
The finite element method in engineering science
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
Journal ArticleDOI
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
Proceedings ArticleDOI
Reducing the bandwidth of sparse symmetric matrices
E. Cuthill,J. McKee +1 more
TL;DR: A direct method of obtaining an automatic nodal numbering scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth is presented.