Showing papers by "Hans-Peter Lenhof published in 1995"

Sequential and parallel algorithms for the k closest pairs problem

Abstract: Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and . A new and simpler proof is given of Salowe’s theorem, i.e., a sequential algorithm is given that computes the k closest pairs in the set S in O(n log n+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. Salowe’s algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM model. This version runs in O((log n)2 log log n) expected parallel time and has an O(n log n log log n+k) time-processor product. Finally, actual running times are given of an implementation of our sequential algorithm.

An algorithm for the protein docking problem

Abstract: We have implemented a parallel distributed geometrie dock.ing algorithm that uses a new measure for the size of the contact area of two moleeules. The measure is a potential function that counts the "van der Waals contacts" between the atoms of the two molecules ( the algorithm does not compute the Lennard-Jones potential). An integer constant C4 is added to the potential for each pair of atoms whose distance is in a certain interval. For each pair whose distance is smaller than the lower bound of the interval an integer constant c~ is subtracted hom the potential (c4 < c~) . The number of allowed overlapping atom pairs is handled by a third parameter N. Conformations where more than N atom pairs overlap are ignored. In our "real world" experiments we have used a small parameter N that allows small loeal penetration. Among the best five dockings found by the algorithm there was almost always a good (rms) approximation of the real conformation. In 42 of 52 test examples the best conformation with respect to the potential function was an approximation of the real conformation. The running time of our sequential algorithm is in the order of the running time of the algorithm of Norel et al. [NLW+]. The parallel version of the algorithm has a reasonable speedup and modest communication requirements.

Maintaining the visibility map of spheres while moving the viewpoint

Abstract: We investigate three-dimensional visibility problems for scenes that consist ofn non-intersecting spheres The viewing point moves on a flightpath that is part of a “circle at infinity” given by a planeP and a range of angles {α(t)¦te[0∶1]} ⊂ [0∶2π] At “time”t, the lines of sight are parallel to the ray inP, which starts in the origin ofP and represents the angleα(t) (orthographic views of the scene) We give an algorithm that computes the visibility graph at the start of the flight, all time parameters at which the topology of the scene changes, and the corresponding topology changes The algorithm has running time0(n + k + p) logn), wheren is the number of spheres in the scene;p is the number of transparent topology changes (the number of different scene topologies visible along the flight path, assuming that all spheres are transparent); andk denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight