An algorithm for computing the restriction scaffold assignment problem in computational biology

Let S and T be two finite sets of points on the real line with |S|+|T|=n and |S|>|T|. The restriction scaffold assignment problem in computational biology assigns each point of S to a point of T such that the sum of all the assignment costs is minimized, with the constraint that every element of T must be assigned at least one element of S. The cost of assigning an element si of S to an element tj of T is |s_i - t_j|, i.e., the distance between si and tj. In 2003 Ben-Dor, Karp, Schwikowski and Shamir [J. Comput. Biol. 10 (2) (2003) 385] published an O(nlogn) time algorithm for this problem. Here we provide a counterexample to their algorithm and present a new algorithm that runs in O(n2) time, improving the best previous complexity of O(n3).