Abstract

Randomized (or probabilistic) algorithms and constructions were applied successfully in many areas of theoretical computer science before they were used widely in computational geometry. Following influential work in the mid-1980s, randomized algorithms became popular in geometry, and now a significant proportion of published research in computational geometry employs randomized algorithms or proof techniques. For many problems the best algorithms known are randomized, and even if both randomized and deterministic algorithms of comparable asymptotic complexity are available, the randomized algorithms are often much simpler and more efficient in an actual implementation. In some cases, the best deterministic algorithm known for a problem has been obtained by “derandomizing” a randomized algorithm.