@MISC{Paredes08graphsfor, author = {Rodrigo Paredes}, title = {Graphs for Metric Space Searching}, year = {2008} }

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Abstract

The problem of Similarity Searching consists in finding the elements from a set which are similar to a given query under some criterion. If the similarity is expressed by means of a metric, the problem is called Metric Space Searching. In this thesis we present new methodologies to solve this problem using graphs G(V,E) to represent the metric database. In G, the set V corresponds to the objects from the metric space and E to a small subset of edges from V × V, whose weights are computed according to the metric of the space under consideration. In particular, we study k-nearest neighbor graphs (knngs). The knng is a weighted graph connecting each element from V —or equivalently, each object from the metric space — to its k nearest neighbors. We develop algorithms both to construct knngs in general metric spaces, and to use