Optimum packing of convex-polygons by a new data structure sequence-table

The convex-polygon packing problem is to arrange given convex-polygons without overlapping each other in a bounding box of minimum area. This paper proposes a new algorithm. A solution space of convex-polygon packings is constructed by a new data-structure called the sequence-table which can represent topological relations between two convex-polygons. The algorithm searches the solution space stochastically for an optimum packing. The solution space has two important properties, i.e. every solution is feasible and an optimal solution is included. In our experiments, the system based on simulated annealing was shown to output highly compacted packings of convex-polygons.