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 ∑i,jwπi,πj|xj−xi|. We present a fast 3-approximation algorithm for the problem. We present a randomized approximation algorithm with a better performance guarantee for the special case where xi=i,i=1,…,n. Finally, we introduce a 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.