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

The restriction scaffold assignment problem takes as input two finite point sets S and T (with S containing more points than 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. An algorithm is presented that finds a minimum-cost solution for this problem in O(n log n) time, provided that the points in S and T are restricted to lie on a line and the cost function δ is the L₁ metric. This algorithm runs in linear time, if S and T are presorted. This improves the previously best-known O(n ²)-time algorithm for this problem.