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An efficient algorithm for embedding exchanged hypercubes into grids

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Abstract

Graph embedding is an important technology in simulating parallel structures and designing VLSI layout. Hypercube is one of the most significant interconnection networks in parallel computing systems. The exchanged hypercube is an important variant of the hypercube, which is obtained by systematically deleting edges from a hypercube. It not only retains several valuable and desirable properties of the hypercube, but also has lower hardware cost. In this paper, we first give an exact formula of minimum wirelength of exchanged hypercube layout into a grid. Furthermore, we propose an O(N) algorithm for embedding exchanged hypercube into a gird with load 1, expansion 1 and minimum wirelength and derive a linear layout of exchanged hypercube with minimum number of tracks and efficient layout areas. Finally, we present simulation experiments of our embedding algorithm on network overhead and total wirelength, which conduce to estimate the total wirelength and chip area.

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Acknowledgements

We would like to express our sincerest appreciation to Prof. Guoliang Chen for his constructive suggestions. This work is supported by National Key R&D Program of China (No. 2018YFB1003201), Natural Science Foundation of China under Grant (Nos. 61572337, 61602333, 61672296, 61702351 and 61872196), Scientific & Technological Support Project of Jiangsu Province (No. BE2016777, BE2016185), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Nos. 17KJB520036 and 18KJA520009) and Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Foundation (No. WSNLBKF201701).

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Authors and Affiliations

  1. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Weibei Fan, Jianxi Fan, Cheng-Kuan Lin, Guijuan Wang & Baolei Cheng

  2. Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing, 210003, Jiangsu Province, China

    Jianxi Fan & Ruchuan Wang

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  1. Weibei Fan
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  2. Jianxi Fan
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  3. Cheng-Kuan Lin
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  4. Guijuan Wang
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Correspondence to Jianxi Fan.

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Fan, W., Fan, J., Lin, CK. et al. An efficient algorithm for embedding exchanged hypercubes into grids. J Supercomput 75, 783–807 (2019). https://doi.org/10.1007/s11227-018-2612-2

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  • DOI: https://doi.org/10.1007/s11227-018-2612-2

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