Line-Constrained Geometric Server Placement

TL;DR

This paper introduces new algorithms for constrained geometric server placement problems, including 1-center and K-median computations on line segments, with applications in distributed systems across various scientific fields.

Contribution

The paper presents novel algorithmic solutions for line-constrained geometric placement problems, expanding the toolkit for distributed system optimization.

Findings

Algorithms for 1-center and obnoxious 1-center on line segments.

Solutions for K-median constrained to a line.

Applications in distributed systems and scientific fields.

Abstract

In this paper we present new algorithmic solutions for several constrained geometric server placement problems. We consider the problems of computing the 1-center and obnoxious 1-center of a set of line segments, constrained to lie on a line segment, and the problem of computing the K-median of a set of points, constrained to lie on a line. The presented algorithms have applications in many types of distributed systems, as well as in various fields which make use of distributed systems for running some of their applications (like chemistry, metallurgy, physics, etc.).