Probabilistic Analysis of Random Extension-Rotation Algorithms

Abstract : We introduce a new random structure generalizing matroids. The random independence systems (RIS) allow us to develop general techniques for solving hard combinatorial optimization problems with random inputs. We describe a randomized algorithm for efficiently constructing an independent set of fixed size in an instance of a random independence system. We provide a general method of analysis of the performance of this algorithm, which allows us to derive bounds on the mean, variance and all the moments of the time complexity of the algorithm. (Author)