Computing the volume of convex bodies : a case where randomness provably helps
نویسنده
چکیده
We discuss the problem of computing the volume of a convex body K in R. We review worst-case results which show that it is hard to deterministically approximate voln K and randomised approximation algorithms which show that with randomisation one can approximate very nicely. We then provide some applications of this latter result. •Supported by NATO grant RG0088/89 t Supported by NSF grant CCR-8900112 and NATO grant RG0088/89
منابع مشابه
Dispersion of Mass and the Complexity of Randomized Algorithms
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex geometry. We obtain a nearly quadratic lower bound on the complexity of randomized volume algorithms for convex bodies in R (the current best algorithm has complexit...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملOn the Complexity of Computing Mixed Volumes
This paper gives various (positive and negative) results on the complexity of the problem of computing and approximating mixed volumes of polytopes and more general convex bodies in arbitrary dimension. On the negative side, we present several #P-hardness results that focus on the difference of computing mixed volumes versus computing the volume of polytopes. We show that computing the volume o...
متن کاملSIZE AND GEOMETRY OPTIMIZATION OF TRUSS STRUCTURES USING THE COMBINATION OF DNA COMPUTING ALGORITHM AND GENERALIZED CONVEX APPROXIMATION METHOD
In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...
متن کاملA Decentralized Online Sortition Protocol
We propose a new online sortition protocol which is decentralized. We argue that our protocol has safety, fairness, randomness, non-reputation and openness properties. Sortition is a process that makes random decision and it is used in competitions and lotteries to determine who is the winner. In the real world, sortition is simply done using a lottery machine and all the participa...
متن کامل