Approximating the Bandwidth for Asteroidal Triple-Free Graphs

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 logn) algorithm to approximate the bandwidth of an AT-free graph within a factor 4 and anO(n+ e) algorithm with a factor 6. For the special cases of permutation graphs and trapezoid graphs we obtain O(n log2 n) algorithms with worst case performance ratio 2. For cocomparability graphs we obtain an O(n + e) algorithm with worst case performance ratio 3. Finally, we show that there is an O(n2 log2 n) algorithm to compute the exact bandwidth of chain graphs.