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Mapping two complete binary trees into the star graph with quick fault recovery

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Abstract

This paper proposes an approach for embedding two complete binary trees (CBT) into ann-dimensional star graph (S n), and provides a fault-tolerant scheme for the trees. First, aCBT with height Σ n m=2 ⌊logm⌋ is embedded into theS n with dilation 3. The height of theCBT is very close to ⌊Σ n m=2 logm⌋, the height of the largest possibleCBT which can be embedded into theS n. Shifting the firstCBT by generating function productg 2 g 3 g 4 g 3, anotherCBT with height Σ n m=2 ⌊logm⌋ can also be embedded into theS n without conflicting with the first one. Moreover, if three-eights of nodes in the firstCBT and all nodes in the secondCBT are faulty, all of them can be recovered. Under the condition that the firstCBT with smaller height (⌊Σ n m=2 logm⌋ − 1) is embedded, all the replacement nodes will be free. As a consequence, even in the case that all nodes in the two trees are faulty, they can be recovered in the smallest number of recovery steps and only with dilation 5.

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Authors and Affiliations

  1. Department of Information Management, National Taiwan Institute of Technology, 10772, Taipei, Taiwan, Republic of China

    Chiun -Chieh Hsu

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  1. Chiun -Chieh Hsu
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Chiun-Chieh Hsu, Ph.D.: He is a full professor of Information Management Department at National Taiwan University of Science and Technology. His current research interests include fault-tolerant computing, parallel and distributed processing, networks, and graph theory. He received his B. E., M. E., and Ph.D. degrees all in electrical engineering from National Taiwan University in 1983, 1987, and 1990, respectively. He worked as a software and firmware design engineer of Research and Development in Acer Computer Company from 1983 to 1985.

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Hsu, C.C. Mapping two complete binary trees into the star graph with quick fault recovery. NGCO 15, 403–419 (1997). https://doi.org/10.1007/BF03037299

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  • DOI: https://doi.org/10.1007/BF03037299

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