We develop the concept of weighted aligned hypergraph bimorphism where the weights may, in particular, represent probabilities. Such a bimorphism consists of an R≥0-weighted regular tree grammar, two hypergraph algebras that interpret the generated trees, and a family of alignments between the two interpretations. Semantically, this yields a set of bihypergraphs each consisting of two hypergrap...

In recent years wavelets were shown to be effective data synopses. We are concerned with the problem of finding efficiently wavelet synopses for massive data sets, in situations where information about query workload is available. We present linear time, I/O optimal algorithms for building optimal workload-based wavelet synopses for point queries. The synopses are based on a novel construction ...

For example, IR with the regular Euclidean distance is a metric space. It is usually of interest to consider the finite case, where X is an n-point set. Then, the function d can be specified by ( n 2 ) real numbers. Alternatively, one can think about (X,d) is a weighted complete graph, where we specify positive weights on the edges, and the resulting weights on the edges comply with the triangl...