Typical properties of winners and losers in discrete optimization

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 combinatorial 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 complexity. Our analysis is...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: René Beier, Berthold Vöcking
• Keywords: Algorithms, Binary Optimization Problems, Combinatorial Optimization Problems, Polynomial Smoothed Complexity, STOC 2004