A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

  • Authors:

  • Chia-Jui Lai;Chang-Hsiung Tsai;Hong-Chun Hsu;Tseng-Kui Li

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Dong Hwa University, Shoufeng, Haulien 97401, Taiwan, ROC;Department of Computer Science and Information Engineering, National Dong Hwa University, Shoufeng, Haulien 97401, Taiwan, ROC;Department of Medical Informatics Tzu Chi University, Haulien 970, Taiwan, ROC;Department of Computer Science and Information Engineering, Ching Yun University, JungLi 320, Taiwan, ROC

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n=6 and 1==2, @?"i"="1^ks"i=n-m, and max"1"==3 if n is odd and m=n-32; otherwise, max"1"==n-2m-1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.