Helly's Theorem: New Variations and Applications

TL;DR

This survey reviews recent developments in Helly-type theorems, highlighting their ongoing influence in computational geometry and optimization over the past decade.

Contribution

It provides an updated overview of new Helly-type theorems and their applications since the last comprehensive survey.

Findings

Recent Helly-type theorems have expanded the theoretical framework.

Applications of Helly's theorems in computational geometry have grown.

Helly's theorems continue to impact optimization techniques.

Abstract

This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems continue to be influential in computational geometry and in optimization.