Optimal distortion embeddings of distance regular graphs into Euclidean spaces

Authors:
Frank Vallentin
Affiliations:
Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

Citing 5
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Abstract

In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite programming and exploiting the algebra structure of the optimization problem so that the question of finding a lower bound of the least distortion is reduced to an analytic question about orthogonal polynomials.