Greedy Algorithms for the Shortest Common Superstring That Are Asymptotically Optimal

There has recently been a resurgence of interest in the shortest common superstring problem due to its important applications in molecular biology (e.g., recombination of DNA) and data compression. The problem is NP-hard, but it has been known for some time that greedy algorithms work well for this problem. More precisely, it was proved in a recent sequence of papers that in the worst case a greedy algorithm produces a superstring that is at most β times (2≤β≤ 4 ) worse than optimal. We analyze the problem in a probabilistic framework, and consider the optimal total overlap O _n ^opt and the overlap O _n ^rg produced by various greedy algorithms. These turn out to be asymptotically equivalent. We show that with high probability , where n is the number of original strings and H is the entropy of the underlying alphabet. Our results hold under a condition that the lengths of all strings are not too short. Received November 1996; revised March 1997.