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The Computer Journal 1994 37(2):124-128; doi:10.1093/comjnl/37.2.124
© 1994 by British Computer Society
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A Greedy Hypercube-Labeling Algorithm

D. Bhagavathi *, C. E. Grosch * and S. Olariu *

Department of Computer Science, Old Dominion University, Norfolk, VA 23529-0162, USA

Due to its attractive topological properties, the hypercube multiprocessor has emerged as one of the architectures of choice when it comes to implementing a large number of computational problems. In many such applications, Gray-code labelings of the hypercube are a crucial prerequisite for obtaining efficient algorithms. We propose a greedy algorithm that, given an n-dimensional hypercube H with N=22 nodes, returns a Gray-code labeling of H, that is, a labeling of the nodes with binary strings of length n such that two nodes are neighbors in the hypercube if, and only if, their labels differ in exactly one bit. Our algorithm is conceptually very simple and runs in O(N log N) time being, therefore, optimal. As it turns out, with a few modifications our labeling algorithm can be used to recognize hypercubes as well.

Received October 26, 1993. accepted December 6, 1993.

* Department of Computer Science, Old Dominion University, Norfolk, VA 23529–0162, USS


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