Dispersing Points on Intervals

TL;DR

This paper presents a linear-time algorithm for optimally dispersing points within disjoint intervals on a line and on a cycle, maximizing the minimum pairwise distance among the points.

Contribution

It introduces a greedy, linear-time solution for the dispersion problem on both a line and a cycle, improving efficiency over previous methods.

Findings

Linear-time algorithm for line intervals

Linear-time solution for cycle intervals

Optimal dispersion maximizing minimum distance

Abstract

We consider a problem of dispersing points on disjoint intervals on a line. Given n pairwise disjoint intervals sorted on a line, we want to find a point in each interval such that the minimum pairwise distance of these points is maximized. Based on a greedy strategy, we present a linear time algorithm for the problem. Further, we also solve in linear time the cycle version of the problem where the intervals are given on a cycle.