Greedy algorithms for the shortest commonsuperstring that are asymtotically optimal

Abstract

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 Ooptn and the overlap Ogrn produced by various greedy algorithms. These turn out to be asymptotically equivalent. We show that in several cases, with high probability [Formula presented] 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. Finally, we provide several generalizations and extensions of our basic result.