Approximation Guarantees for the Minimum Linear Arrangement Problem by Higher Eigenvalues

Suguru Tamaki, Yuichi Yoshida

Abstract: Given an undirected graph G = (V,E) and positive edge weights {w e } e ∈ E , a linear arrangement is a permutation π: V → [n]. The value of the arrangement is \(\mathbf{val}(G,\pi):= \frac{1}{n}\sum_{e=\{u,v\}}w_e |\pi(u)-\pi(v)|\). In the minimum linear arrangement problem (MLA), the goal is to find a linear arrangement π * that achieves val(G,π *) = MLA(G): =  min π val(G,π).