Computation of the Hausdorff distance between sets of line segments in parallel

TL;DR

This paper presents a parallel algorithm to compute the Hausdorff distance between two sets of non-intersecting line segments in logarithmic squared time using linear processors, addressing a key step involving extremal intersection points.

Contribution

It introduces a parallel algorithm for Hausdorff distance computation that efficiently handles extremal intersection points between sets of monotone curve segments, improving on previous sequential methods.

Findings

Achieves $O( ext{log}^2 n)$ parallel time with $O(n)$ processors.

Provides a parallel solution for extremal intersection point detection.

Completes Hausdorff distance computation efficiently in parallel.

Abstract

We show that the Hausdorff distance for two sets of non-intersecting line segments can be computed in parallel in $O(\log^2 n)$ time using O(n) processors in a CREW-PRAM computation model. We discuss how some parts of the sequential algorithm can be performed in parallel using previously known parallel algorithms; and identify the so-far unsolved part of the problem for the parallel computation, which is the following: Given two sets of $x$-monotone curve segments, red and blue, for each red segment find its extremal intersection points with the blue set, i.e. points with the minimal and maximal $x$-coordinate. Each segment set is assumed to be intersection free. For this intersection problem we describe a parallel algorithm which completes the Hausdorff distance computation within the stated time and processor bounds.