Approximation Algorithms for Maximum Linear Arrangement

Abstract

The generalized maximum linear arrangement problem is to compute for a given vector x ∈ ℝⁿ and an n x n non-negative symmetric matrix w = (w _i,j), a permutation ? of 1,...,n that maximizes σ_i,j w _{π i},_{π j} |x_j- x_i|. We present a fast 1/3-approximation algorithm for the problem. We also introduce a 12-approximation algorithm for max k-cut with given sizes. This matches the bound obtained by Ageev and Sviridenko, but without using linear programming.