Incremental and Decremental Maintenance of Planar Width

TL;DR

This paper introduces a dynamic algorithm for maintaining the width of a planar point set efficiently during insertions and deletions, with near-linear update times depending on the change in the convex hull.

Contribution

The paper presents a novel algorithm that efficiently updates the planar width under dynamic point set modifications, improving upon previous methods.

Findings

Update time is O(kn^epsilon) per operation.

Amortized update time is O(n^epsilon) for incremental/decremental sequences.

Algorithm handles dynamic changes with near-linear complexity.

Abstract

We present an algorithm for maintaining the width of a planar point set dynamically, as points are inserted or deleted. Our algorithm takes time O(kn^epsilon) per update, where k is the amount of change the update causes in the convex hull, n is the number of points in the set, and epsilon is any arbitrarily small constant. For incremental or decremental update sequences, the amortized time per update is O(n^epsilon).