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

TL;DR

This paper presents an efficient O(n log n)-time algorithm for solving the restricted scaffold assignment problem when points are on a line, improving computational efficiency for this specific case.

Contribution

The paper introduces a novel O(n log n) algorithm for the scaffold assignment problem with points restricted to a line, achieving faster solutions.

Findings

Algorithm runs in O(n log n) time for line-restricted points

Linear time complexity if points are pre-sorted

Significant improvement over previous methods

Abstract

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).