We find recurring amino-acid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein three-dimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; secon...

We examine the problem of computing exactly the Delaunay graph (and the dual Voronoi diagram) of a set of, possibly intersecting, smooth convex pseudo-circles in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) closed curves, every pair of which has at most two intersection points. We propose robust end efficient algorithms for all required predicates under the exact c...

We present some algorithms which construct a triangular graph given a set of points, where each face of the graph complies with the Delaunay criteria. Then we develop an linear time algorithm to construct the contour of such a triangular graph, where each face is coloured either black or white. Our techniques avoid expensive trigonometric computations. We intoduce our algorithms for the 2-dimen...

The location of sensor nodes is an indispensable component for both network operation and sensor data integrity. In this paper we study the network localization problem for a largescale sensor network with a complex shape. We do not assume any anchor nodes with known locations and use only network connectivity information to recover the relative positioning of all the nodes. Thus we require no ...

Consider a weighted graph G where vertices are points in the plane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length of the path produced by the algorithm from any vertex s to any vertex t is at most c times the length of the shortest path from s to t in G. If the length o...

This work presents two generalizations of the algorithm for obtaining a constrained Delaunay triangulation of a general planar graph presented in Vig97] and Vig95]. While the rst generalization works with elliptical distances, the second one can deal with a set of deforming ellipses associated to each point of the plane. The pseudo-code of the procedures involved in the algorithms is included, ...

1 Starting from a maximum-entropy model of granular statics, this brief note explores a possible material instability in the form of a ”stress localization” anticipated in previous work (Goddard, 2002). After a brief review of the maximum-entropy model, it is shown that a special case allows for non-convex pressure-volume response of a kind that could lead to heterogeneous stress states in an i...

Let P be a finite set of points in the plane and S a set of non-crossing line segments with endpoints in P . The visibility graph of P with respect to S, denoted Vis(P, S), has vertex set P and an edge for each pair of vertices u, v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose e...

For a finite set X of points in the plane, a set S in the plane, and a positive integer k, we say that a k-element subset Y of X is captured by S if there is a homothetic copy S′ of S such that X ∩ S′ = Y , i.e., S′ contains exactly k elements from X. A k-uniform S-capturing hypergraph H = H(X,S, k) has a vertex set X and a hyperedge set consisting of all kelement subsets of X captured by S. In...