FRESH: Fr\'echet Similarity with Hashing

TL;DR

FRESH is an approximate hashing-based method for efficient r-range search of curves under the continuous Fréchet distance, balancing speed and accuracy through curve simplification and probabilistic candidate detection.

Contribution

The paper introduces FRESH, a novel approximate, randomized hashing approach for efficient r-range search under the continuous Fréchet distance, with practical pruning techniques.

Findings

FRESH achieves high performance with relaxed precision and recall.

Experimental results show competitive speed compared to exact methods.

Curve simplification effectively reduces computational complexity.

Abstract

This paper studies the $r$-range search problem for curves under the continuous Fr\'echet distance: given a dataset $S$ of $n$ polygonal curves and a threshold $r>0$, construct a data structure that, for any query curve $q$, efficiently returns all entries in $S$ with distance at most $r$ from $q$. We propose FRESH, an approximate and randomized approach for $r$-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. We experimentally compare \fresh to exact and deterministic solutions, and we show that high performance can be reached by suitably relaxing precision and recall.