An Approximation Algorithm for Solving the Problem of Packing Unit Equilateral Triangles in A Square

Polygon packing problem is not only of great theoretical significance but also of wide application prospeces. Since it is NP hard and also a continuous problem, it is very often that the placements of polygons are restricted in advance, for example, no rotation is allowed, and then the solutions are optimized to get a better approximate one. In this paper, a new idea is applied to a special case of polygon packing problem-the problem of packing unit equilateral triangles in a square. The concepts of rigid placements of a triangle and the rigid placement policy are proposed and elaborated, and an algorithm called least destroying algorithm for solving the problem is also given. Complexity analysis and computational results show that the least destroying algorithm is efficient. Based on this algorithm, an efficient algorithm for solving polygon packing problem may be developed.