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The Computer Journal 1996 39(4):331-345; doi:10.1093/comjnl/39.4.331
© 1996 by British Computer Society
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Enhanced Fibonacci Cubes

H. Qian * and J. Wu *

Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, FL, 33431, USA

We propose the enhanced Fibonacci cube (EFC) structure for parallel systems. It is defined based on the sequence Fn = 2Fn–2+2Fn–4. We show that the enhanced Fibonacci cube contains the Fibonacci cube (FC) as a subgraph and maintains virtually all the desirable properties of the Fibonacci cube. In addition, it is a Hamiltonian graph. We can embed complete binary trees into enhanced Fibonacci cubes with dilation one and with a relatively small expansion. We also propose a series of enhanced Fibonacci cubes EFC(k), where k is a series number. Each EFC(k) contains an FC of the same order as a subcube. Moreover, each EFC(k) in the series contains any other cube that precedes it as subcubes and the last one in the series is a hypercube of the corresponding order. This series of EFC(k)s provides us with more options for selecting cubes with various sizes. Because EFC is a subgraph of the hypercube, it may find applications in fault-tolerant computing for degraded hypercube computer systems. As an application of EFC, we show that the parallel prefix sum computation can be efficiently implemented on enhanced Fibonacci cubes.

Received November 2, 1994. revised March 17, 1996.

* Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, FL, 33431, USA Email: jie{at}sunrise.cse.fau.edu


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