Absolute o(logm) error in approximating random set covering: an average case analysis

This work concerns average case analysis of simple solutions for random set covering (SC) instances. Simple solutions are constructed via an O(nm) algorithm. At first an analytical upper bound on the expected solution size is provided. The bound in combination with previous results yields an absolute asymptotic approximation result of o(logm) order. An upper bound on the variance of simple solution values is calculated. Sensitivity analysis performed on simple solutions for random SC instances shows that they are highly robust, in the sense of maintaining their feasibility against augmentation of the input data with additional random constraints.