Approximating the Bandwidth for Asteroidal Triple-Free Graphs

@article{Kloks1995ApproximatingTB,
  title={Approximating the Bandwidth for Asteroidal Triple-Free Graphs},
  author={Ton Kloks and Dieter Kratsch and Haiko M{\"u}ller},
  journal={J. Algorithms},
  year={1995},
  volume={32},
  pages={41-57}
}
We show that there is an O(n3) algorithm to approximate the bandwidth of an AT-free graph with worst case performance ratio 2. Alternatively, at the cost of the approximation factor, we can also obtain an O(e+n log n) algorithm to approximate the bandwidth of an AT-free graph within a factor 4. For the special cases of permutation graphs and trapezoid graphs we obtain O(n log n) algorithms with worst case performance ratio 2. For cocomparability graphs we obtain an O(n2) algorithm with worst… 
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57 Citations
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57 Citations

Approximating Bandwidth by Mixing Layouts of Interval Graphs
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On Claw-Free Asteroidal Triple-Free Graphs
Improved bandwidth approximation for trees
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A simple randomized O(log 2 n lov~-n)-approximation algorithm for bandwidth minimization on trees is presented.
On Approximation Hardness of the Bandwidth Problem
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It is shown that there are no efficient polynomial time approximation schemes for the bandwidth problem under some plausible assumptions, and that there is no polynometric time approximation algorithms with an absolute error guarantee of n^{1-epsilon} for any epsilon <0 unless P=NP.
NP-Hardness of the Bandwidth Problem onDense Graphs ( Revised )
TLDR
This paper proves that the bandwidth problem on the dense instances remains NP-hard.
Treewidth and Minimum Fill-in on d-Trapezoid Graphs
TLDR
Each of the four graph parameters can be computed in time O(n 2 ) for trapezoid graphs and thus for permutation graphs even if no intersection model is part of the input.
Interval Completion with the Smallest Max-degree
TLDR
The interval degree of a graph is defined to be the smallest max-degree of any of its interval supergraphs and it is proved that for any graph G the interval degree is at least the bandwidth, the pathwidth of G2 and at most twice the bandwidth of G.
NP-Hardness of the Bandwidth Problem onDense
TLDR
This paper proves that the bandwidth problem on the dense instances of dense graphs remains NP-hard.
Interval degree and bandwidth of a graph
The complexity of the approximation of the bandwidth problem
  • Walter Unger
  • Computer Science, Mathematics
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
TLDR
The bandwidth problem has a long history and a number of important applications and it is shown for any constant k/spl epsiv/N that there is no polynomial time approximation algorithm with an approximation factor of k, and that this result holds also for caterpillars, a class of restricted trees.
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