Affiliation:
1. School of Computer Science, University of Sydney, Darlington, NSW, Australia
Abstract
We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fréchet distance. Given an
n
vertex trajectory
P
and an
m
vertex query trajectory
Q
, we seek to
report
a vertex-aligned sub-trajectory
P
′ of
P
that is closest to
Q
, i.e.,
P′
must start and end on contiguous vertices of
P
. Since in real data
P
typically contains a
very large
number of vertices, we focus on answering queries, without restrictions on
P
or
Q
, using only precomputed structures of
𝒪(n)
size.
We use three baseline algorithms from straightforward extensions of known work; however, they have impractical performance on realistic inputs. Therefore, we propose a new Hierarchical Simplification Tree (HST) data structure and an adaptive clustering-based query algorithm that efficiently explores relevant parts of
P
. The core of our query methods is a novel greedy-backtracking algorithm that solves the Fréchet decision problem using
𝒪(n+m)
space and
𝒪O(nm)
time in the worst case.
Experiments on real and synthetic data show that our heuristic effectively prunes the search space and greatly reduces computations compared to baseline approaches.
Funder
Australian Research Council Discovery Projects funding scheme
Publisher
Association for Computing Machinery (ACM)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Computer Science Applications,Modeling and Simulation,Information Systems,Signal Processing