Approximating the Bandwidth for Asteroidal Triple-Free Graphs

Abstract

We show that there is an O(nm) 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(m+nlogn) 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(nlog2n) algorithms with worst-case performance ratio 2. For cocomparability graphs we obtain an O(n+m) algorithm with worst-case performance ratio 3.