A layout adjustment problem for disjoint rectangles preserving orthogonal order

Abstract

AbstractThis study considers a set of n rectangles arranged on a plane, and, in particular, the problem of modifying the initial layout within a minimum area while meeting certain conditions, namely, preservation of orthogonal order and prevention of intersection between rectangles. A heuristic algorithm for this problem with O(n2) complexity was proposed by Misue and colleagues. First, the problem of minimum‐area layout adjustment is shown to be NP‐complete. Then, another heuristic algorithm is examined that results in smaller layout area than that of Misue and colleagues. Using computational experiments with random initial layouts, the proposed algorithm is proven to require 15 to 20% of the area required by the Misue algorithm, especially with a large number of rectangles. © 2002 Scripta Technica, Syst Comp Jpn, 33(2): 31–42, 2002