Approximation Algorithms for Maximum Linear Arrangement

The GENERALIZED MAXIMUM LINEAR ARRANGEMENT PROBLEM is to compute for a given vector x ∈ Rn and an n × n non-negative symmetric matrix w = (wi,j), a permutation π of {1, ..., n} that maximizes Σi,j wπi, πj |xj - xi|. We present a fast 1/3-approximation algorithm for the problem. We also introduce a 1/2-approximation algorithm for MAX k-CUT WITH GIVEN SIZES. This matches the bound obtained by Ageev and Sviridenko, but without using linear programming.