## Compaction Algorithms for Non-Convex Polygons and Their Applications (1994)

Citations: | 27 - 2 self |

### BibTeX

@MISC{Li94compactionalgorithms,

author = {Zhenyu Li},

title = {Compaction Algorithms for Non-Convex Polygons and Their Applications},

year = {1994}

}

### OpenURL

### Abstract

Given a two-dimensional, non-overlapping layout of convex and non-convex polygons, compaction refers to a simultaneous motion of the polygons that generates a more densely packed layout. In industrial two-dimensional packing applications, compaction can improve the material utilization of already tightly packed layouts. Efficient algorithms for compacting a layout of non-convex polygons are not previously known. This dissertation offers the first systematic study of compaction of non-convex polygons. We start by formalizing the compaction problem as that of planning a motion that minimizes some linear objective function of the positions. Based on this formalization, we study the complexity of compaction and show it to be PSPACE-hard. The major contribution of this dissertation is a position-based optimization model that allows us to calculate directly new polygon positions that constitute a locally optimum solution of the objective via linear programming. This model yields the first ...