Approximation Algorithms for Maximum Linear Arrangement

The generalized maximum linear arrangement problem is to compute for a given vector x 2 IR n and an n n non-negative symmetric matrix W = (w i;j), a permutation of f1; :::; ng that maximizes P i;j w i ;; j jx j ? x i j. We present a fast 1 3-approximation algorithm for the problem. We present a randomized approximation algorithm with a better performance guarantee for the special case where x i = i i = 1 2-approximation algorithm for max k-cut with given sizes of parts. This matches the bound obtained by Ageev and Sviridenko, but without using linear programming.