On the probable performance of Heuristics for bandwidth minimization
SIAM Journal on Computing
Graphs with small bandwidth and cutwidth
Discrete Mathematics
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
Theoretical Computer Science - Selected papers in honor of Manuel Blum
A Comparison of Several Bandwidth and Profile Reduction Algorithms
ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
A new matrix bandwidth reduction algorithm
Operations Research Letters
Multilevel algorithms for linear ordering problems
Journal of Experimental Algorithmics (JEA)
Phase Transition in the Bandwidth Minimization Problem
MICAI '09 Proceedings of the 8th Mexican International Conference on Artificial Intelligence
Compression of digital road networks
SSTD'07 Proceedings of the 10th international conference on Advances in spatial and temporal databases
Decorous Lower Bounds for Minimum Linear Arrangement
INFORMS Journal on Computing
Hi-index | 0.01 |
Finding a linear layout of a graph having minimum bandwidth is a combinatorial optimization problem that has been studied since the 1960s. Unlike other classical problems, the approach based on stating a suitable integer linear program and solving the associated linear-programming relaxation seems to be useless in this case. This makes it nontrivial to design algorithms capable of solving to optimality instances of reasonable size. In this paper, we illustrate a new simple lower bound on the optimal bandwidth and its extension within an enumerative algorithm, leading to integer linear-programming relaxations that can be solved efficiently and provide effective lower bounds if part of the layout is fixed. Keeping the integrality constraints in these relaxations is essential for this purpose. We show that the resulting method can solve to proven optimality 24 out of the 30 instances from the literature with less than 200 nodes, each in less than a minute on a personal computer. The new approach is also analyzed on randomly generated instances with up to 1,000 nodes. Moreover, we propose a method to compute the well-known density lower bound on the optimal bandwidth, which succeeds in finding this bound within minutes for most instances in the literature with up to 250 nodes.