Graph Search Approach to Rectangle Packing Problem

Abstract

A rectangle packing problem is considered, where the goal is to suitably arrange a subset of given rectangles within a container so that the area of wastes (uncovered spaces) is the smallest. We propose a reduction of this problem to a graph search problem and show possible solving approaches by means of well known BFS, Dijkstra’s and A_ algorithms. We explain the way we construct search graphs for the problem, taking under consideration two main variants: (1) with arbitrary straight-line cuts, (2) with straight-line cuts which must go along the whole length or width of the remaining container — ‘full cuts’. We also give some insights on: optimization criterion, search stopping condition and heuristics we use. Finally, we present results of experiments carried out