On the Greedy Superstring Conjecture

We investigate the greedy algorithm for the shortest common superstring problem. We show that the length of the greedy superstring is upper-bounded by the sum of the lengths of an optimal superstring and an optimal cycle cover, provided the greedy algorithm happens to merge the strings in a particular way. Thus, when restricting inputs correspondingly, we verify the well known greedy conjecture, namely that the approximation ratio of the greedy algorithm is within a factor of two of the optimum, and actually extend the conjecture considerably. We achieve this bound by systematically combining known conditional inequalities about overlaps, periodand string-lengths with a new familiy of string inequalities. We show that conventional systems of conditional inequalities, including the Monge inequalities, are insufficient to obtain our result. AMS subject classification: 68W05, 68W25, 68W40