An Efficient Construction of Yao-Graph in Data-Distributed Settings

TL;DR

This paper presents a new algorithm for constructing Yao-graphs, a type of geometric spanner, in massively parallel computation settings, significantly reducing time and memory compared to previous methods.

Contribution

It introduces an efficient MPC algorithm for Yao-graph construction using range trees, improving time and memory efficiency over prior approaches.

Findings

Achieves near-linear total time complexity

Reduces total memory usage to subquadratic levels

Provides a scalable method for geometric spanner construction

Abstract

A sparse graph that preserves an approximation of the shortest paths between all pairs of points in a plane is called a geometric spanner. Using range trees of sublinear size, we design an algorithm in massively parallel computation (MPC) model for constructing a geometric spanner known as Yao-graph. This improves the total time and the total memory of existing algorithms for geometric spanners from subquadratic to near-linear.