Typical properties of winners and losers in discrete optimization

Rene Beier, Berthold Vöcking
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
We present a probabilistic analysis for a large class of combinatorial optimization problems containing, e.g., all binary optimization problems defined by linear constraints and a linear objective function over {0, 1} n . By parameterizing which constraints are of stochastic and which are of adversarial nature, we obtain a semirandom input model that enables us to do a general average-case analysis for a large class of optimization problems while at the same time taking care for the
more » ... l structure of individual problems. Our analysis covers various probability distributions for the choice of the stochastic numbers and includes smoothed analysis with Gaussian and other kinds of perturbation models as a special case. In fact, we can exactly characterize the smoothed complexity of optimization problems in terms of their random worstcase complexity. A binary optimization problem has a polynomial smoothed complexity if and only if it has a pseudopolynomial com-
doi:10.1145/1007352.1007409 dblp:conf/stoc/BeierV04 fatcat:2bwg7ny4yfcu3kzt3sne3p5f5u