Abstract

A linear arrangement ? of an undirected graph G = (V, E) with ?V? = n nodes is a bijective function ?:V ? {0, … , n ? 1}. The cost function is cost(G,?)=?uv?E(?(u)?(v)) and opt(G) = min??cost(G, ?). The problem of finding opt(G) is called minimum linear arrangement (MINLA). The Minimum Linear Arrangement is an NPhard problem in general. But there are some classes of graphs optimally solvable in polynomial time. In this paper, we show that the label of each node equals to the reverse of binary representation of its id in the optimal arrangement. Then, we design an O(n) algorithm to solve the minimum linear arrangement problem of Chord graphs.
