Evaluating the Reverse Greedy Algorithm

This paper present two meta heuristics, reverse greedy and future aware greedy, which are variants of the greedy algorithm. Both are based on the observation that guessing the impact of future selections is useful for the current selection. While the greedy algorithm makes the best local selection given the past, future aware greedy makes the best local selection given the past and the estimated future, and reverse greedy executes a number of greedy iterations and chooses the last one as the next choice. Future aware greedy depends on a future aware utility function which is problem specific. While we have found such utility functions for the set cover problem this paper concentrate on reverse greedy whose description is truly problem independent. Both algorithms suggested, while not quite as efficient computationally as the greedy algorithm, are still very efficient. We show interesting problems on which the greedy algorithm has been extensively studied where the suggested algorithms outperform greedy. We also show a problem with different characteristics on which the greedy algorithm is better and try to categorize the kind of problems for which future aware and reverse greedy are expected to yield good result.