Hypercube Embedding of Distances with Few Values Hypercube Embedding of Distances with Few Values
نویسنده
چکیده
A distance d on a nite set V is hypercube embeddable if it can be isometrically embedded into the hypercube f0; 1g m for some m 1, i.e., if the elements i 2 V can be labeled by sets A i in such a way that d(i; j) = jA i 4A j j for all i; j 2 V. Testing whether a distance d is hypercube embeddable is an NP-complete problem, even if d is assumed to take its values in f2; 3; 4; 6g ((Chv80]). On the other hand, the hypercube embeddability problem is polynomial when restricted to the class of distances with values in f1; 2; 3g ((Avi90]). Let x; y be positive integers such that exactly two of x; y; x+y are odd. We show that, for xed x; y, the hypercube embeddability problem remains polynomial for the class of distances with values in fx; y; x + yg.
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