Abstract
Abstract We present an optimal greedy algorithm which returns a Gray-code labeling of the nodes of an n -dimensional hypercube; that is, a labeling of the nodes with binary strings of length n for which the Hamming distance between two nodes is 1 if and only if these are adjacent in the hypercube. The proposed algorithm is very simple; it uses breadth-first search to guide the greedy choice of nodes and computes the Gray-code label of a node u by performing the logical disjunction of the Gray-code labels of two nodes adjacent to node u . It takes as input a hypercube Q n with N =2 n nodes and runs in O( N log N ) time. Based on the labeling algorithm we propose a recognition algorithm for hypercubes which runs in O( N log N ) time. Thus, in view of the fact that Q n has n 2 n −1 edges, this behaviour is optimal. Both labeling and recognition algorithms incorporate such algorithmic features that they can be optimally implemented in a PRAM model of computation.
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