Abstract
The binary hypercube, although a versatile multiprocessor network, has a draw back: its size must be a power of two. In order to alleviate this draw back, we define the concept of an n-node Compact Hypercube CH(n) which deals with the problem of computation with incomplete hypercubes. We show how to construct a hypercube like structure for any number n that can be easily upgraded to a complete hypercube. This concept allows the algorithms to work efficiently even if hypercubes are incomplete. Development of algorithms on compact hypercubes further allow us to efficiently execute several algorithms concurrently on a complete hypercube.
In this paper, we restrict our investigation to the graph properties and recognition algorithms for compact hypercubes. We show that compact hypercubes exhibit many properties which are common with complete hypercubes. We also present results on efficient representation and counting of compact hypercubes within a complete hypercube.
Research Supported in part by fellowships from the Faculty Research and Creative Activities Support Fund WMU-FRCASF 90-15 and WMU-FRCASF 89-225274, and by the National Science Foundation under grant USE-90-52346.
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© 1991 Springer-Verlag Berlin Heidelberg
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Boals, A.J., Gupta, A.K., Hashmi, J.A., Sherwani, N.A. (1991). Compact hypercubes: Properties and recognition. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_187
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DOI: https://doi.org/10.1007/3-540-54029-6_187
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