The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Graphs with small bandwidth and cutwidth
Discrete Mathematics
Computing the bandwidth of interval graphs
SIAM Journal on Discrete Mathematics
On finding the minimum bandwidth of interval graphs
Information and Computation
Bandwidth of theta graphs with short paths
Discrete Mathematics
An $0(n \log n)$ Algorithm for Bandwidth of Interval Graphs
SIAM Journal on Discrete Mathematics
Approximating the bandwidth via volume respecting embeddings
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Improved bandwidth approximation for trees and chordal graphs
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating Bandwidth by Mixing Layouts of Interval Graphs
SIAM Journal on Discrete Mathematics
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
Bandwidth of Split and Circular Permutation Graphs
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
The Complexity of the Approximation of the Bandwidth Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Measured Descent: A New Embedding Method for Finite Metrics
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Volume distortion for subsets of Euclidean spaces: extended abstract
Proceedings of the twenty-second annual symposium on Computational geometry
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
Approximating the bandwidth of caterpillars
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Bandwidth of convex bipartite graphs and related graphs
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Bandwidth of convex bipartite graphs and related graphs
Information Processing Letters
A novel parameterised approximation algorithm for minimum vertex cover
Theoretical Computer Science
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The bandwidth of an n-vertex graph G is the minimum value b such that the vertices of G can be mapped to distinct integer points on a line without any edge being stretched to a distance more than b. Previous to the work reported here, it was known that it is NP-hard to approximate the bandwidth within a factor better than 3/2. We improve over this result in several respects. For certain classes of graphs (such as cycles of cliques) for which it is easy to approximate the bandwidth within a factor of 2, we show that approximating the bandwidth within a ratio better than 2 is NP-hard. For caterpillars (trees in which all vertices of degree larger than two lie on one path) we show that it is NP-hard to approximate the bandwidth within any constant, and that an approximation ratio of clogn/loglogn will imply a quasi-polynomial time algorithm for NP (when c is a sufficiently small constant).