Shortest Consistent Superstrings Computable in Polynomial Time

The shortest consistent superstring problem is, given a set of positive strings and a set of negative strings, finding a shortest string including every positive string and no negative string as a substrin& This problem is NP-hard and arises in DNA sequencing by hybridization. It is also an extension of the well-known shortest cotillion superstring problem which corresponds to the case when the set of negative strings is empty. In this paper we show that a shortest consistent superstring can be found in polynomial time if(i) a longest common nonsupetstring for the set of negative strings exists or (ii) the number of positive strings is bounded and every symbol of the alphabet appears at the end of some negative string, in the case (i) a longest consistent superstring can also be found in polynomial time.