On approximating arbitrary metrices by tree metrics

We design a generation algorithm for a problem which a&es in computational chemistry: the random generation of models of amorphous strutures. Such structures can be modeled as graphs which see embedded in d-space. The algorithm uses the well known approach of simulating a rapidly-mixing Markov chain. Gur analysis of the Mixing rate is based on Dobrushin uniqueness. The structure of the problem forces us to extend the basic method and find an alternative to Dobrushin’s condition which is more appropriate for our problem. This extension appears to be of more general interest.

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