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This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by “walking through” the triangulation, after selecting a “good starting point” by random sampling. The analysis generalizes and extends a recent result for d = 2 dimensions by proving(More)
Given two convex polygons P and Q we want to find a line segment (a bridge) that connects P and Q so that the maximum distance from a point inside P across the bridge to a point inside Q is minimized. We propose a linear-time algorithm to solve this problem, improving the O(n2 log(n)) algorithm described by Cai, Xu and Zhu [Inform. Process. Lett. 69 (1999)(More)
The paper “The Approximability of the Exemplar Breakpoint Distance Problem” [1], which appeared in AAIM 2006, contained several negative results and one positive result — a claimed O(log n)factor greedy approximation for the One-sided Exemplar Breakpoint Distance Problem. Here, we show that the analysis was incorrect and the approximation factor of the(More)
This short note considers the problem of point location in a Delaunay triangulation of n random points, using no additional preprocessing or storage other than a standard data structure representing the triangulation. A simple and easy-to-implement (but, of course, worst-case suboptimal) heuristic is shown to take expected time O(n 1/3 ) .
We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both(More)
Map labeling is an important problem in Geographical Information Systems (GIS). This problem is well studied in the area of cartography, especially using heuristics and logic programming [Y072, Imh75, Jon89, DF92, CMS93, BC94]. The study of map labeling problem from the algorithmic point of view starts very recently. In general, map labeling problems are(More)
Map labeling is of fundamental importance in cartography and geographical information systems and is one of the areas targeted for research by the ACM Computational Geometry Impact Task Force. Previous work on map labeling has focused on the problem of placing maximal uniform, axis-aligned, disjoint rectangles on the plane so that each point feature to be(More)
In this paper we report our research on building WebSail, an intelligent web search engine that is able to perform real-time adaptive learning. WebSail learns from the user's relevance feedback, so that it is able to speed up its search process and to enhance its search performance. We design an efficient adaptive learning algorithm TW2 to search for web(More)