Simple, efficient maxima-finding algorithms for multidimensional samples

TL;DR

This paper introduces simple, efficient algorithms for finding maxima in multidimensional data, analyzing their expected complexity, comparing them with existing methods, and demonstrating their practical applications.

Contribution

It presents new, easy-to-implement algorithms for multidimensional maxima finding, with analyzed performance and practical applications in sequence analysis.

Findings

Algorithms are simple and easily coded.

Expected complexity analyzed.

Compared favorably with existing methods.

Abstract

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The expected complexity of some measures related to the performance of the algorithms is analyzed. We also compare the efficiency of the algorithms with a few major ones used in practice, and apply our algorithms to find the maximal layers and the longest common subsequences of multiple sequences.