The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Computing the bandwidth of interval graphs
SIAM Journal on Discrete Mathematics
On finding the minimum bandwidth of interval graphs
Information and Computation
An $0(n \log n)$ Algorithm for Bandwidth of Interval Graphs
SIAM Journal on Discrete Mathematics
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Information Processing Letters
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
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
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
Worst-case study of local search for MAX-k-SAT
Discrete Applied Mathematics - The renesse issue on satisfiability
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques
Theory of Computing Systems
Volume Distortion for Subsets of Euclidean Spaces
Discrete & Computational Geometry
Efficient approximation of min set cover by moderately exponential algorithms
Theoretical Computer Science
Approximating the Bandwidth of Caterpillars
Algorithmica
Approximation of min coloring by moderately exponential algorithms
Information Processing Letters
Exponential-time approximation of weighted set cover
Information Processing Letters
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Bandwidth of bipartite permutation graphs in polynomial time
Journal of Discrete Algorithms
Set Partitioning via Inclusion-Exclusion
SIAM Journal on Computing
An Exponential Time 2-Approximation Algorithm for Bandwidth
Parameterized and Exact Computation
Approximating the max-edge-coloring problem
Theoretical Computer Science
Exact and approximate bandwidth
Theoretical Computer Science
Discrete Applied Mathematics
Bandwidth of convex bipartite graphs and related graphs
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
ACM Transactions on Algorithms (TALG)
Bandwidth and distortion revisited
Discrete Applied Mathematics
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized approximation problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity and Approximation Algorithms
The Computer Journal
Hi-index | 5.23 |
The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797^n)=O(3^0^.^6^2^1^7^n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have O^*(3^n) and O^*(2^n) worst-case running time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident to vertices in the same bucket or to vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a divide-and-conquer strategy along with dynamic programming to achieve the improved time bound.