Approximating the Bandwidth for Asteroidal Triple-Free Graphs

  title={Approximating the Bandwidth for Asteroidal Triple-Free Graphs},
  author={Ton Kloks and Dieter Kratsch and Haiko M{\"u}ller},
  journal={J. Algorithms},
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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A bandwidth approximation algorithm is obtained that executes in O(n log2 n) time and has performance ratio 2, which is the best possible performance ratio of any polynomial time bandwidth approximation algorithms for circular-arc graphs.
Improved bandwidth approximation for trees
A simple randomized O(log 2 n lov~-n)-approximation algorithm for bandwidth minimization on trees is presented.
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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.
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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.
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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
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
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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  • A. Sprague
  • Computer Science, Mathematics
    SIAM J. Discret. Math.
  • 1994
This paper presents an algorithm for the bandwidth problem on interval graphs given an interval model for an interval graph with n vertices and an integer and constructs a layout of bandwidth at most $k$ if there exists one.
Computing the bandwidth of interval graphs
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We present a linear-time algorithm for sparse symmetric matrices which converts a matrix into pentadiagonal form (“bandwidth 2”), whenever it is possible to do so using simultaneous row and column
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  • J. Spinrad
  • Computer Science, Mathematics
    SIAM J. Comput.
  • 1985
The orientation algorithm can be used to reduce the problem of recognizing comparability graphs to that of recognizing transitive graphs, and gives an upper bound of $O(n^{2.49 + } )$ for comparability graph recognition.
The bandwidth problem for graphs and matrices - a survey
This survey describes all the results known to the authors as of approximately August 1981 and describes the effect on bandwidth of local operations such as refinement and contraction of graphs, bounds on bandwidth in terms of other graph invariants, the bandwidth of special classes of graph, and approximate bandwidth algorithms for graphs and matrices.
Bandwidth of theta graphs with short paths
Complexity of finding embeddings in a k -tree
This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.
A Linear Time Algorithm to Compute a Dominating Path in an AT-Free Graph