Computing a Subtrajectory Cluster from c-packed Trajectories

We present a near-linear time approximation algorithm for the subtrajectory cluster problem of $c$-packed trajectories. The problem involves finding $m$ subtrajectories within a given trajectory $T$ such that their Fr\'echet distances are at most $(1 + \varepsilon)d$, and at least one subtrajectory must be of length~$l$ or longer. A trajectory $T$ is $c$-packed if the intersection of $T$ and any ball $B$ with radius $r$ is at most $c \cdot r$ in length. Previous results by Gudmundsson and Wong \cite{GudmundssonWong2022Cubicupperlower} established an $\Omega(n^3)$ lower bound unless the Strong Exponential Time Hypothesis fails, and they presented an $O(n^3 \log^2 n)$ time algorithm. We circumvent this conditional lower bound by studying subtrajectory cluster on $c$-packed trajectories, resulting in an algorithm with an $O((c^2 n/\varepsilon^2)\log(c/\varepsilon)\log(n/\varepsilon))$ time complexity

Efficient motif discovery in spatial trajectories using discrete Fréchet distance

National Research Foundation (NRF) Singapore under International Research Centres in Singapore Funding Initiativ

Locality-Sensitive Hashing of Curves

We study data structures for storing a set of polygonal curves in ${\rm R}^d$ such that, given a query curve, we can efficiently retrieve similar curves from the set, where similarity is measured using the discrete Fr\'echet distance or the dynamic time warping distance. To this end we devise the first locality-sensitive hashing schemes for these distance measures. A major challenge is posed by the fact that these distance measures internally optimize the alignment between the curves. We give solutions for different types of alignments including constrained and unconstrained versions. For unconstrained alignments, we improve over a result by Indyk from 2002 for short curves. Let $n$ be the number of input curves and let $m$ be the maximum complexity of a curve in the input. In the particular case where $m \leq \frac{\alpha}{4d} \log n$, for some fixed $\alpha>0$, our solutions imply an approximate near-neighbor data structure for the discrete Fr\'echet distance that uses space in $O(n^{1+\alpha}\log n)$ and achieves query time in $O(n^{\alpha}\log^2 n)$ and constant approximation factor. Furthermore, our solutions provide a trade-off between approximation quality and computational performance: for any parameter $k \in [m]$, we can give a data structure that uses space in $O(2^{2k}m^{k-1} n \log n + nm)$, answers queries in $O( 2^{2k} m^{k}\log n)$ time and achieves approximation factor in $O(m/k)$.Comment: Proc. of 33rd International Symposium on Computational Geometry (SoCG), 201

Fast trajectory search for real-world applications

With the popularity of smartphones equipped with GPS, a vast amount of trajectory data are being produced from location-based services, such as Uber, Google Maps, and Foursquare. We broadly divide trajectory data into three types: 1) commuter trajectories from taxicabs and ride-sharing apps; 2) vehicle trajectories from GPS navigation apps; 3) activity trajectories from social network check-ins and travel blogs. We investigate efficient and effective search on each of the three types of trajectory data, each of which has a real-world application. In particular: 1) commuter trajectory search can serve for the transport capacity estimation and route planning; 2) vehicle trajectory search can help real-time traffic monitoring and trend analysis; 3) activity trajectory search can be used in interactive and personalized trip planning. As the most straightforward trajectory data, a commuter trajectory only contains two points: origin and destination indicating a passenger’s movement, which is valuable for transportation decision making. In this thesis, we propose a novel query RkNNT to estimate the capacity of a bus route in the transport network. Answering RkNNT is challenging due to the high amount of data from commuters. We propose efficient solutions to prune most trajectories which cannot choose a query route as their nearest one. Further, we apply RkNNT to the optimal route planning problem-MaxRkNNT. A vehicle trajectory has more points than a commuter trajectory, as it tracks the whole trace of a vehicle and can further advocate the application of traffic monitoring. We conclude the common queries over trajectory data for monitoring purposes and proposes a search engine Torch to manage and search trajectories with map matching over a road network, instead of storing raw data sampled from GPS with a high cost. Besides improving the efficiency of search, Torch also supports compression, effectiveness evaluation of various existing similarity measures, and large-scale clustering k-paths with a novel similarity measure LORS. Exploring the activity trajectory data which contains textual information can help plan personalized trips for tourists. Based on spatial indexes which we propose for commuter and vehicle trajectory data, we further develop a unified search paradigm to process various top-k queries over activity trajectory and POIs data (hotels, restaurants, and attractions, etc.) at the same time. In particular, a new point-wise similarity measure PATS and an indexing framework with a unified search paradigm are proposed

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum