Polynomial Time Algorithms for Bichromatic Problems

TL;DR

This paper introduces polynomial time algorithms for solving bichromatic geometric problems, extending techniques from monochromatic cases and addressing applications in machine learning and data mining.

Contribution

The paper develops novel polynomial time algorithms for bichromatic geometric problems, expanding existing methods from monochromatic to bichromatic scenarios.

Findings

Algorithms are polynomial time and exact.

Techniques are novel and potentially broadly applicable.

Addresses problems relevant to machine learning and data mining.

Abstract

In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear naturally and frequently in the fields like Machine learning, Data mining, and so on, and (ii) we are interested in extending the algorithms and techniques for single point set (monochromatic) problems to bichromatic case. For all the problems considered in this paper, we design low polynomial time exact algorithms. These algorithms are based on novel techniques which might be of independent interest.