Improved Map Construction using Subtrajectory Clustering

Buchin, Kevin; Buchin, Maike; Gudmundsson, Joachim; Hendriks, J Jimi; Sereshgi, Erfan Hosseini; Sacristán, Vera; Silveira, Rodrigo I.; Sleijster, Jorrick; Staals, Frank; Wenk, Carola

doi:10.1145/3423334.3431451

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…We show, in the continuous case, an O(n 3 log 2 n) time algorithm and a 3OV-hardness lower bound, and in the discrete case, an O(n 2 log n) time algorithm and a quadratic lower bound. Our bounds are almost tight unless SETH fails.1 Buchin et al [8] show an O(|S| • n 2 ) time algorithm, where S is the set of (internal) critical points. In this paper, we show that |S| = Θ(n 3 ), yielding an overall running time of O(n 5 ).…”

mentioning

confidence: 76%

“…They reported common movements of the ball, common movements of football players, and correlations between players in the same team moving together. Buchin et al [8] applied subtrajectory clustering to map reconstruction. They reconstructed the location of roads, turns and crossings from urban vehicle trajectories, and the location of hiking trails from hiking trajectories.…”

Section: Introductionmentioning

confidence: 99%

“…The most closely related result is by Buchin et al [9]. Their algorithm forms the basis of several implementations [7,8,18,19,20]. Other models of algorithm for trajectories of any dimension.…”

Section: Introductionmentioning

confidence: 99%

“…1 Buchin et al [8] show an O(|S| • n 2 ) time algorithm, where S is the set of (internal) critical points. In this paper, we show that |S| = Θ(n 3 ), yielding an overall running time of O(n 5 ).…”

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confidence: 99%

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Cubic upper and lower bounds for subtrajectory clustering under the continuous Fréchet distance

Gudmundsson¹,

Wong²

2021

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Detecting commuting patterns or migration patterns in movement data is an important problem in computational movement analysis. Given a trajectory, or set of trajectories, this corresponds to clustering similar subtrajectories.We study subtrajectory clustering under the continuous and discrete Fréchet distances. The most relevant theoretical result is by Buchin et al. (2011). They provide, in the continuous case, an O(n 5 ) time algorithm 1 and a 3SUM-hardness lower bound, and in the discrete case, an O(n 3 ) time algorithm. We show, in the continuous case, an O(n 3 log 2 n) time algorithm and a 3OV-hardness lower bound, and in the discrete case, an O(n 2 log n) time algorithm and a quadratic lower bound. Our bounds are almost tight unless SETH fails.1 Buchin et al. [8] show an O(|S| • n 2 ) time algorithm, where S is the set of (internal) critical points. In this paper, we show that |S| = Θ(n 3 ), yielding an overall running time of O(n 5 ).

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confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Cubic upper and lower bounds for subtrajectory clustering under the continuous Fréchet distance

Gudmundsson¹,

Wong²

2021

Preprint

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“…The algorithmic ideas presented in [9] were implemented and extended by Gudmundsson and Valladares [19] who obtained practical speed ups using GPUs. In a series of papers, these ideas were also applied to the problem of reconstructing road maps from GPS data [7,8]. In a similar vain, Buchin, Kilgus and Kölzsch [10] studied the trajectories of migrating animals and defined so-called group diagrams which are meant to represent the underlying migration patterns in the form of a graph.…”

Section: Related Workmentioning

confidence: 99%

Faster Approximate Covering of Subcurves under the Fréchet Distance

Frederik¹,

Jacobus²,

Driemel³

2022

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Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of a set cover problem for a given polygonal curve: find the smallest number k of representative curves such that any point on the input curve is contained in a subcurve that has Fréchet distance at most a given ∆ to a representative curve. We focus on the case where the representative curves are line segments and approach this NP-hard problem with classical techniques from the area of geometric set cover: we use a variant of the multiplicative weights update method which was first suggested by Brönniman and Goodrich for set cover instances with small VC-dimension. We obtain a bicriteria-approximation algorithm that computes a set of O(k log(k)) line segments that cover a given polygonal curve of n vertices under Fréchet distance at most O(∆). We show that the algorithm runs in O(k 2 n + kn 3 ) time in expectation and uses O(kn + n 3 ) space. For two dimensional input curves that are c-packed, we bound the expected running time by O(k 2 c 2 n) and the space by O(kn + c 2 n). In R d the dependency on n instead is quadratic. In addition, we present a variant of the algorithm that uses implicit weight updates on the candidate set and thereby achieves near-linear running time in n without any assumptions on the input curve, while keeping the same approximation bounds. This comes at the expense of a small (polylogarithmic) dependency on the relative arclength.

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