The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
STOC '94 Proceedings of the twenty-sixth 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
On Euclidean Embeddings and Bandwidth Minimization
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Practical fast polynomial multiplication
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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
Approximating the Bandwidth of Caterpillars
Algorithmica
Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
An Exponential Time 2-Approximation Algorithm for Bandwidth
Parameterized and Exact Computation
ACM Transactions on Algorithms (TALG)
An exact algorithm for minimum distortion embedding
Theoretical Computer Science
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Bandwidth and distortion revisited
Discrete Applied Mathematics
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating MAX SAT by moderately exponential and parameterized algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Deterministic parameterized connected vertex cover
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Algorithms for dominating clique problems
Theoretical Computer Science
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Efficient algorithms for the max k-vertex cover problem
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
Fast algorithms for min independent dominating set
Discrete Applied Mathematics
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
| Hi-index | 5.23 |
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 an O(n^O^(^t^)2^n) exact algorithm. Moreover, for any two positive integers k=2,r=1, we present a (2kr-1)-approximation algorithm that solves Bandwidth for an arbitrary input graph in O^*(k^n^(^k^-^1^)^r) time and polynomial space where by O^* we denote the standard big O notation but omitting polynomial factors. Finally, we improve the currently best known exact algorithm for arbitrary graphs with an O(4.383^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 Bjorklund 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.