Improved bandwidth approximation for trees
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Coping with the NP-Hardness of the Graph Bandwidth Problem
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Bandwidth of Split and Circular Permutation Graphs
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Interval degree and bandwidth of a graph
Discrete Applied Mathematics
Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Algorithms for graphs with small octopus
Discrete Applied Mathematics
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph bandwidth of weighted caterpillars
Theoretical Computer Science - Algorithmic applications in management
Particle Swarm Optimization and Hill Climbing for the bandwidth minimization problem
Applied Intelligence
Laying Out Sparse Graphs with Provably Minimum Bandwidth
INFORMS Journal on Computing
Graph-Theoretic Concepts in Computer Science
Exact and Approximate Bandwidth
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
On the Cubicity of AT-Free Graphs and Circular-Arc Graphs
Graph Theory, Computational Intelligence and Thought
Bandwidth of bipartite permutation graphs in polynomial time
Journal of Discrete Algorithms
Ant colony optimization with hill climbing for the bandwidth minimization problem
Applied Soft Computing
Approximating bandwidth by mixing layouts of interval graphs
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Bandwidth of bipartite permutation graphs in polynomial time
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Exact and approximate bandwidth
Theoretical Computer Science
Hardness results for approximating the bandwidth
Journal of Computer and System Sciences
Low Distortion Maps Between Point Sets
SIAM Journal on Computing
On maximum differential graph coloring
GD'10 Proceedings of the 18th international conference on Graph drawing
ACM Transactions on Algorithms (TALG)
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
Graph bandwidth of weighted caterpillars
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Optimal linear arrangement of interval graphs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
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The bandwidth problem has a long history and a number of important applications. It is the problem of enumerating the vertices of a given graph $G$ such that the maximum difference between the numbers of adjacent vertices is minimal. We will show for any constant $k\in\nat$ that there is no polynomial time approximation algorithm with an approximation factor of $k$. Furthermore, we will show that this result holds also for caterpillars, a class of restricted trees. We construct for any $x,\epsilon\in\rel$ with $x1$ and $\epsilon0$ a graph class for which an approximation algorithm with an approximation factor of $x+\epsilon$ exists, but the approximation of the bandwidth problem within a factor of $x-\epsilon$ is NP-complete. The best previously known approximation factors for the intractability of the bandwidth approximation problem were $1.5$ for general graphs and $4/3$ for trees.