Rectilinear drawing of a graph on a plane with the minimum number of line segments

Abstract

A riveted graph G(V,E) is a graph whose vertices are fixed on a plane. Its rectilinear drawing D(G) is a configuration of G on the plane in such a way that every edge is composed of horizontal and vertical line segments. The authors consider the problem of reducing the number of line segments and present an algorithm to obtain such a rectilinear drawing that the total number of line segments is no more than 3 mod E mod . It is noted that a drawing so obtained contains no edge composed of five line segments. The algorithm runs in O( mod E mod ) time and space. >