Detecting Commuting Patterns by Clustering Subtrajectories

Buchin, Kevin; Buchin, Maike; Gudmundsson, Joachim; Löffler, Maarten; Luo, Jun

doi:10.1142/s0218195911003652

Cited by 117 publications

(124 citation statements)

References 27 publications

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“…One popular form of processing of the gathered data is information summarization, in particular, trajectory clustering; for some recent work see, e.g., [9] and references thereof.…”

Section: Related Workmentioning

confidence: 99%

Optimizing airspace closure with respect to politicians' egos

Kostitsyna

Löffler

Polishchuk

2015

Theoretical Computer Science

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When a president is landing at a busy airport, the airspace around the airport closes for commercial traffic. We show how to schedule the presidential squadron so as to minimize its impact on scheduled civilian flights; to obtain an efficient solution we use a "rainbow" algorithm recoloring aircraft on the fly as they are stored in a special type of forest. We also give a data structure to answer the following query efficiently: Given the president's ego (the requested duration of airspace closure), when would be the optimal time to close the airspace? Finally, we study the dual problem: Given the time when the airspace closure must start, what is the longest ego that can be tolerated without sacrificing the general traffic? We solve the problem by drawing a Christmas tree in a delay diagram; the tree allows one to solve also the query version of the problem.

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“…One popular form of processing of the gathered data is information summarization, in particular, trajectory clustering; for some recent work see, e.g., [9] and references thereof.…”

Section: Related Workmentioning

confidence: 99%

Optimizing airspace closure with respect to politicians' egos

Kostitsyna

Löffler

Polishchuk

2015

Theoretical Computer Science

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“…Second category of online compression techniques perform encoding of points along with eliminating redundant points [8]- [10,20]. In [20] Frchet distance is used to cluster popular subtrajectories in a given trajectory dataset.…”

Section: Related Workmentioning

confidence: 99%

Trajectory Approximation for Resource Constrained Mobile Sensor Networks

Murtaza

Kanhere

Ignjatović

et al. 2014

2014 IEEE International Conference on Distributed Computing in Sensor Systems

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Abstract-Low-power compact sensor nodes are being increasingly used to collect trajectory data from moving objects such as wildlife. The size of this data can easily overwhelm the data storage available on these nodes. Moreover, the transmission of this extensive data over the wireless channel may prove to be difficult. The memory and energy constraints of these platforms underscores the need for lightweight online trajectory compression albeit without seriously affecting the accuracy of the mobility data. In this paper, we present a novel online Polygon Based Approximation (PBA) algorithm that uses regular polygons, the size of which is determined by the allowed spatial error, as the smallest spatial unit for approximating the raw GPS samples. PBA only stores the first GPS sample as a reference. Each subsequent point is approximated to the centre of the polygon containing the point. Furthermore, a coding scheme is proposed that encodes the relative position (distance and direction) of each polygon with respect to the preceding polygon in the trajectory. The resulting trajectory is thus a series of bit codes, that have pair-wise dependencies at the reference point. It is thus possible to easily reconstruct an approximation of the original trajectory by decoding the chain of codes starting with the first reference point. Encoding a single GPS sample is an O(1) operation, with an overall complexity of O(n). Moreover, PBA only requires the storage of two raw GPS samples in memory at any given time. The low complexity and small memory footprint of PBA make it particularly attractive for low-power sensor nodes. PBA is evaluated using GPS traces that capture the actual mobility of flying foxes in the wild. Our results demonstrate that PBA can achieve up to nine-fold memory savings as compared to DouglasPeucker line simplification heuristic. While we present PBA in the context of low-power devices, it can be equally useful for other GPS-enabled devices such smartphones and car navigation units.

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“…Most known approximation algorithms make further assumptions on the curves, and only an O(n 2 )-time approximation algorithm is known for arbitrary polygonal curves [24]. The Fréchet distance and its variants, such as dynamic timewarping [13], have found various applications, with recent work particularly focusing on geographic applications such as map-matching tracking data [15,63] and moving objects analysis [19,20,47].…”

Section: Introductionmentioning

confidence: 99%

Four Soviets Walk the Dog: Improved Bounds for Computing the Fréchet Distance

Buchin

Meulemans

et al. 2017

Discrete Comput Geom

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Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One popular measure is the Fréchet distance. Since it was proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original O(n 2 log n) algorithm by Alt and Godau for computing the Fréchet distance remains the state of the art (here, n denotes the number of edges on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUM-hard. In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Fréchet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fréchet distance between two polygonal curves in time O(n 2 √ log n(log log n) 3/2 ) on a pointer machine and in time O(n 2 (log log n) 2 ) on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth O(n 2−ε ), for some ε > 0. We believe that this reveals an intriguing new aspect of this well-studied problem. Finally, we show how to obtain the first subquadratic algorithm for computing the weak Fréchet distance on a word RAM.

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Detecting Commuting Patterns by Clustering Subtrajectories

Cited by 117 publications

References 27 publications

Optimizing airspace closure with respect to politicians' egos

Optimizing airspace closure with respect to politicians' egos

Trajectory Approximation for Resource Constrained Mobile Sensor Networks

Four Soviets Walk the Dog: Improved Bounds for Computing the Fréchet Distance

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