Efficient algorithms for computing distances between one-dimensional point sets

• Main Author: Colannino, Justin
• Format: Others
• Language: en
• Published: McGill University 2005
• Subjects: Computer Science.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=84019

Let S and T denote sets of points on the line with the total number of points equal to n. In this thesis the focus is on computing distance measures between S and T as defined by different types of assignments . An assignment is a function, F, which pairs elements of the two sets together. In particular, we are interested in the distances given by two types of assignment. When F is a surjection between the sets, the surjection distance minimizes the sum of the costs of the pairings. When the assignment is restricted only by the property that all elements in both sets must be paired at least once, the corresponding distance measure is referred to as the link distance. After a review of the literature on assignments, including an in depth description of a foundational result for assignments on the line published by Karp and Li in 1975, new algorithms are presented which improve the computational complexity of both the surjection and link distances for one-dimensional sets. In 2003 Ben-Dor et al. proposed a O(n log n) algorithm for the surjection distance in one-dimension. We provide a counter-example to their algorithm as well as a new algorithm which has a complexity of O(n 2), improving the previous best O(n3) result of Eiter and Mannila. Our algorithm for the link distance in one-dimension also runs in O(n 2) time, improving the previous best complexity of O(n 3) also due to Eiter and Mannila.