Randomized Algorithms for Geometric Optimization Problems

This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We review a number of general techniques, including randomized binary search, randomized linear-programming algorithms, and random sampling. Next, we describe several applications of these techniques, including facility location, proximity problems, nearest neighbor searching, statistical estimators, and Euclidean TSP. Work by the rst author was supported by Army Research O ce MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by NSF grants EIA{9870724, EIA{997287, and CCR{9732787, and by a grant from the U.S.-Israeli Binational Science Foundation. y Center for Geometric Computing, Department of Computer Science, Box 90129, Duke University, Durham, NC 27708-0129, USA. E-mail: [email protected] z Department of Computer Science and Engineering, IIT Delhi, New Delhi 110016, India. Email:[email protected]