The general problem of finding the shortest superstring to a given number of strings (that is, the shortest string such that all given strings appear as substrings) is NP-complete. The authors, with Blum, Tromp, and Yannakakis [1], have shown that several greedy algorithms yield O ( n ) superstrings, where n is the theoretical optimum, on the condition that no substrings are forbidden. The authors modify some of their previous algorithms to allow negative strings that may not appear as substrings in the superstring, in the two cases that either no negative string contains an admissible substring, or the number of negative strings is constant. Using Monge’s principle [2] that in any optimal solution of a transport problem no two paths may intersect, they prove by a lengthy series of elementary combinatorial and counting lemmas that their greedy algorithm yields a superstring of length O ( n^4&slash;3 ). They conjecture that ultimately a polynomial-time algorithm yielding an O ( n ) superstring is possible. As an aside, in the Computing Reviews classification, “linear” means what it usually means in mathematics. These authors use “linear” as a synonym for “O ( n ),” which means “having an upper bound that is linear in some (nonlinearly defined) variable,” which definitely is not linear.