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Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex s to all the other vertices of P, calculation of the subpolygon of P consisting… (More)

diagrams of set-theoretic solid models. A retraction" method for planning the motion of a disk.

We present linear time algorithms for solving the following problems involving a simple planar polygon <italic>P</italic>: (i) Computing the collection of all shortest paths inside <italic>P</italic> from a given source vertex <italic>s</italic> to all the other vertices of <italic>P</italic>; (ii) Computing the subpolygon of <italic>P</italic> consisting… (More)

Given a convex polygonal robot B with k edges capable of translation and rotation, and a set of polygonal obstacles {A 1 ,. .. , A m } each with n i sides and n = m i=1 n i , Leven and Sharir [1] prove that the number of critical placements of B at which it makes 3 simultaneous contacts with the obstacles but does not intersect their interior is O(knλ 6… (More)

We present a relatively simple algorithm which runs in time &Ogr;(n<supscrpt>2</supscrpt>log n) for the above mentioned problem. The algorithm is an optimized variant of the decomposition technique of the configuration space of the ladder, due to Schwartz and Sharir. The algorithm is based on some ideas which may be exploited to improve the efficiency of… (More)

We present efficient algorithms for the following geometric problems: (i) Preprocessing of a 2-D polyhedral terrain so as to support fast ray shooting queries from a fixed point. (ii) Determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations. (iii) Determining whether a given convex polygon… (More)

- J T Schwartz, M Sharir, D Leven, An, Planning, Ceg +18 others
- 1992

A survey of motion planning and related geometric algorithms. ecient simple motion planning algorithm for a ledder moving in two-dimensional space amidst polygonal barriers. a purely translational motion for a convex object in two-dimensional space using generalizaed voronoi diagrams. A singly exponential stratication scheme for real semi-algebraic… (More)

- Kevin Black, Harvey Mudd, Daniel Leven
- 2010

We derive a new upper bound of 26 for the Ramsey number R(K 5 − P 3 , K 5), lowering the previous upper bound of 28. This leaves 25 ≤ R(K 5 − P 3 , K 5) ≤ 26, improving on one of the three remaining open cases in Hendry's table, which listed Ramsey numbers for pairs of graphs (G, H) with G and H having five vertices. We also show, with the help of a… (More)