Recognizing binary Hamming graphs inO(n
2 logn) time |
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Authors: | F Aurenhammer J Hagauer |
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Affiliation: | (1) Institute für Informationsverarbeitung, Technische Universität Graz, Graz, Austria |
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Abstract: | A graphG is called a binary Hamming graph if each vertex ofG can be assigned a binary address of fixed length such that the Hamming distance between two addresses equals the length of a shortest path between the corresponding vertices. It is shown thatO(n
2 logn) time suffices for deciding whether a givenn-vertex graphG is a binary Hamming graph, and for computing a valid addressing scheme forG provided it exists. This is not far from being optimal asn addresses of lengthn — 1 have to be computed in the worst case. |
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Keywords: | |
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