This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development

relationships; the third, fold, describes geometrical relationships. The distinction between evolutionary relationships and those that arise from the physics and chemistry of proteins is a feature that is unique to this database, so far. The database can be used as a source of data to calibrate sequence search

, errors of substitution, and correlation between occurrences. Analyses of these data attempt to explain the observed similarity relations and to capture the underlying structure of the objects under study. The theoretical analysis of similarity relations has been dominated by geometric models

to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings

Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded

. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” two-dimensional transform that can capture the intrinsic geometrical structure

term memory processes for intensifying and diversifying the search. Included are illustrative data structures for implementing the tabu conditions (and associated aspiration criteria) that underlie these processes. Part I concludes with a discussion of probabilistic tabu search and a summary

the evolution of such groups largely unresolved: what are the structural features that influence whether individuals will join communities, which communities will grow rapidly, and how do the overlaps among pairs of communities change over time? Here we address these questions using two large sources of data

deliver fundamentally higher bandwidth and reliability relative to typical tree structures. This paper presents Bullet, a scalable and distributed algorithm that enables nodes spread across the Internet to self-organize into a high bandwidth overlay mesh. We construct Bullet around the insight that data