We show that the well-known random incremental construction of Clarkson and Shor can be adapted via {\it gradations} to provide efficient external-memory algorithms for some geometric problems. In particular, as the main result, we obtain an optimal randomized algorithm for the problem of computing the trapezoidal decomposition determined by a set of $N$ line segments in the plane with $K$ pairwise intersections, that requires $\Theta(\frac{N}{B} \log_{M/B} \frac{N}{B} +\frac{K}{B})$ expected disk accesses, where $M$ is the size of the available internal memory and $B$ is the size of the block transfer. The approach is sufficiently general to obtain algorithms also for the problems of 3-d half-space intersections, 2-d and 3-d convex hulls, ...
Randomized incremental construction (RIC) is one of the most important paradigms for building geomet...
Abstract: The combination of divide-and-conquer and random sampling has proven very effective in the...
We describe general randomized reductions of certain geometric optimization problems to their corres...
We show that the well-known random incremental construction of Clarkson and Shor can be adapted via ...
This paper presents a very simple incremental randomized algorithm for computing the trapezoidal dec...
AbstractThis paper presents a very simple incremental randomized algorithm for computing the trapezo...
We present further applications of random sampling techniques which have been used for deriving eff...
We present parallel algorithms for some fundamental problems in computational geometry which have a ...
AbstractThis paper presents a very simple incremental randomized algorithm for computing the trapezo...
We introduce a new randomized sampling technique, called Polling which has applications to deriving ...
AbstractWe describe the first optimal randomized in-place algorithm for the basic 3-d convex hull pr...
We present parallel algorithms for some fundamental problems in computational geometry which have ru...
Blockwise access to data is a central theme in the design of efficient external memory (EM) algorith...
The ability to manipulate objects in computer graphics and robotics depends critically on fast and f...
In this paper we first prove the following combinatorial bound, concerning the complexity of the ver...
Randomized incremental construction (RIC) is one of the most important paradigms for building geomet...
Abstract: The combination of divide-and-conquer and random sampling has proven very effective in the...
We describe general randomized reductions of certain geometric optimization problems to their corres...
We show that the well-known random incremental construction of Clarkson and Shor can be adapted via ...
This paper presents a very simple incremental randomized algorithm for computing the trapezoidal dec...
AbstractThis paper presents a very simple incremental randomized algorithm for computing the trapezo...
We present further applications of random sampling techniques which have been used for deriving eff...
We present parallel algorithms for some fundamental problems in computational geometry which have a ...
AbstractThis paper presents a very simple incremental randomized algorithm for computing the trapezo...
We introduce a new randomized sampling technique, called Polling which has applications to deriving ...
AbstractWe describe the first optimal randomized in-place algorithm for the basic 3-d convex hull pr...
We present parallel algorithms for some fundamental problems in computational geometry which have ru...
Blockwise access to data is a central theme in the design of efficient external memory (EM) algorith...
The ability to manipulate objects in computer graphics and robotics depends critically on fast and f...
In this paper we first prove the following combinatorial bound, concerning the complexity of the ver...
Randomized incremental construction (RIC) is one of the most important paradigms for building geomet...
Abstract: The combination of divide-and-conquer and random sampling has proven very effective in the...
We describe general randomized reductions of certain geometric optimization problems to their corres...