The minimum linear arrangement problem on proper interval graphs

We present a linear time algorithm for the minimum linear arrangement problem on proper interval graphs. The obtained ordering is a 4-approximation for general interval graphs. 1 Preliminaries Let F be a family of nonempty sets. The intersection graph of F is obtained by representing each set in F by a vertex and connecting two vertices by an edge if and only if their corresponding sets intersenct. The intersection graph of a family of intervals on a linearly ordered set (like the real line) is called an interval graph. If these intervals are constructed such that no interval properly contains another then such graph is called a proper interval graph. The families of interval and proper interval graphs are widely studied and used in different fields. In this chapter we present an algorithm which produces an optimal solution of the MinLA on proper interval graphs. Let us construct graph G = (V, E) in a following way (algorithm A):

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Ilya Safro
• Keywords: CORR 2006, Education, Intersection Graph, Interval Graphs, Proper Interval Graphs