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Abstract and Applied Analysis
Volume 2014, Article ID 308474, 8 pages
http://dx.doi.org/10.1155/2014/308474
Research Article

A New Quasi-Human Algorithm for Solving the Packing Problem of Unit Equilateral Triangles

1School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China
2Optical Instrument Workshop, 95107 Troops, Guangzhou 510500, China
3Informatization Office, University of Shanghai for Science and Technology, Shanghai 200093, China
4Zhengzhou Xinda Jiean Information Technology Co., Ltd, Zhengzhou 450002, China

Received 3 June 2014; Accepted 9 July 2014; Published 5 August 2014

Academic Editor: Zidong Wang

Copyright © 2014 Ruimin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The packing problem of unit equilateral triangles not only has the theoretical significance but also offers broad prospects in material processing and network resource optimization. Because this problem is nondeterministic polynomial (NP) hard and has the feature of continuity, it is necessary to limit the placements of unit equilateral triangles before optimizing and obtaining approximate solution (e.g., the unit equilateral triangles are not allowed to be rotated). This paper adopts a new quasi-human strategy to study the packing problem of unit equilateral triangles. Some new concepts are put forward such as side-clinging action, and an approximation algorithm for solving the addressed problem is designed. Time complexity analysis and the calculation results indicate that the proposed method is a polynomial time algorithm, which provides the possibility to solve the packing problem of arbitrary triangles.