An O(n log n)-Time Algorithm for the Restricted Scaffold Assignment

The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)-time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).Comment: 13 pages, 8 figure

Proximity-graph-based tools for DNA clustering

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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 s i of S to an element t j of T is |s i - t j |, i.e., the distance between s i and t j . In 2003 Ben-Dor, Karp, Schwikowski and Shamir [2] published an O(n logn) time algorithm for this problem. Here we provide a counter-example to their algorithm and present a new algorithm that runs in O(n ) time, improving the best previous complexity of O(n )