Planar linear arrangements of outerplanar graphs

Given an n-vertex outerplanar graph G, the problem is considered of arranging the vertices of G on a line so that no two edges cross and various cost measures are minimized. Efficient algorithms are presented for generating layouts in which every edge (i, j) and of G does not exceed a given bandwidth b(i, j), and the total edge length and the cutwidth of the layout are minimized. Characterizations of optimal layouts used by the algorithms are given. The algorithms combine sublayouts by solving two processor-scheduling problems. Although these scheduling problems are generally NP-complete, the instances generated by the algorithms are polynomial in n