On the greedy superstring conjecture

Abstract

We investigate the greedy algorithm for the shortest common superstring problem. For a restricted class of orders in which strings are merged, we show that the length of the greedy superstring is upper-bounded by the sum of the length of an optimal superstring and an optimal cycle cover. Thus in this restricted setting we verify the well known conjecture, that the performance ratio of the greedy algorithm is within a factor of two of the optimum and actually extend the conjecture considerably. We achieve this by systematically combining known conditional inequalities about overlaps, period- and string-lengths, with a new familiy of string inequalities. It can be shown that conventional systems of conditional inequalities, including the Monge inequalities are insufficient to obtain our result. © Springer-Verlag Berlin Heidelberg 2003.