Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric

TL;DR

This paper introduces a discrepancy-sensitive approach to dynamic fractional cascading, providing efficient data structures for dominated maxima searching and nearest neighbor queries in the plane under any Minkowski metric.

Contribution

It presents novel dynamic data structures that improve efficiency for maxima searching and nearest neighbor queries in the plane, adaptable to any Minkowski metric.

Findings

Efficient dynamic data structure for dominated maxima searching.

Effective nearest neighbor queries in any Minkowski metric.

Improved performance over previous methods.

Abstract

This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric.