Improved Performance of the Greedy Algorithm for the Minimum Set Cover and Minimum Partial Cover Problems

We establish signiicantly improved bounds on the performance of the greedy algorithm for approximating minimum set cover and minimum partial cover. Our improvements result from a new approach to both problems. In particular, (a) we improve the known bound on the performance ratio of the greedy algorithm for general covers without cost, showing that it diiers from the classical harmonic bound by a function which approaches innnity (as the size of the base set increases); (b) we show that, for covers without cost, the performance guarantee for the greedy algorithm is signiicantly better than the performance guarantee for the randomized rounding algorithm; (c) we prove that the classical bounds on the performance of the greedy algorithm for complete covers with costs are valid for partial covers as well, thus lowering, by more than a factor of two, the previously known estimate.