The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Coping with the NP-Hardness of the Graph Bandwidth Problem
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Graph-Theoretic Concepts in Computer Science
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Capacitated domination faster than O(2n)
Information Processing Letters
Theoretical Computer Science
Bandwidth and distortion revisited
Discrete Applied Mathematics
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
| Hi-index | 0.00 |
In this paper we gather several improvements in the field of exact and approximate exponential-time algorithms for the Bandwidth problem. For graphs with treewidth t we present a O (n O (t ) 2 n ) exact algorithm. Moreover for the same class of graphs we introduce a subexponential constant-approximation scheme --- for any *** 0 there exists a (1 + *** )-approximation algorithm running in $O(\exp(c(t + \sqrt{n/\alpha})\log n))$ time where c is a universal constant. These results seem interesting since Unger has proved that Bandwidth does not belong to APX even when the input graph is a tree (assuming P *** NP). So somewhat surprisingly, despite Unger's result it turns out that not only a subexponential constant approximation is possible but also a subexponential approximation scheme exists. Furthermore, for any positive integer r , we present a (4r *** 1)-approximation algorithm that solves Bandwidth for an arbitrary input graph in $O^*(2^{n\over r})$ time and polynomial space. Finally we improve the currently best known exact algorithm for arbitrary graphs with a O (4.473 n ) time and space algorithm. In the algorithms for the small treewidth we develop a technique based on the Fast Fourier Transform, parallel to the Fast Subset Convolution techniques introduced by Björklund et al. This technique can be also used as a simple method of finding a chromatic number of all subgraphs of a given graph in O *(2 n ) time and space, what matches the best known results.