Learn More
Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of(More)
We present a simple randomized algorithm which solves linear programs with <italic>n</italic> constraints and <italic>d</italic> variables in expected <italic>O</italic>(<italic>nde</italic><supscrpt>(<italic>d</italic> ln(<italic>n</italic>+1))<supscrpt>1/4</supscrpt></supscrpt>) time in the unit cost model (where we count the number of arithmetic(More)
In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “on-line” than earlier similar methods, takes expected timeO(nℝgn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and(More)
This paper investigates the computational complexity of planning the motion of a body B in 2-D or 3-D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence(More)
Davenport-Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport-Schinzel sequence composed of n symbols is 6(noc(n»), where t1.(n)is the functional inverse of Ackermann's function, and is thus very(More)
We consider the problem of computing the shortest path between two points in two- or three-dimensional space bounded by polyhedral surfaces. In the 2-D case the problem is easily solved in time <italic>O</italic>(<italic>n</italic><supscrpt>2</supscrpt> log <italic>n</italic>).In the general 3-D case the problem is quite hard to solve, and is not even(More)
We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their(More)