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Documents authored by Kuijpers, Bart

Document
DOI: 10.4230/LIPIcs.TIME.2025.12
On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases

Authors: Arthur Jansen and Bart Kuijpers

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Trajectory sample databases store finite sequences of measured space-time locations of moving objects, along with a speed bound for each object. These databases can be seen as uncertain databases. We propose a language that allows the formulation of queries about the uncertainty in trajectory sample databases. As part of that language, we introduce the notion of visit events, which are used to describe certain constraints on the movement of an object. In our language, an atomic query asks whether a moving object can, given its limitations, realise such an event. We give complexity results for this realisability problem, in various settings.
Cite as

Arthur Jansen and Bart Kuijpers. On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases. In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.TIME.2025.12,
  author =	{Jansen, Arthur and Kuijpers, Bart},
  title =	{{On the Complexity of the Realisability Problem for Visit Events in Trajectory Sample Databases}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.12},
  URN =		{urn:nbn:de:0030-drops-244586},
  doi =		{10.4230/LIPIcs.TIME.2025.12},
  annote =	{Keywords: Trajectory sample databases, uncertain databases, query languages, complexity}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.TIME.2025.16
Solutions to the Generalised Alibi Query in Moving Object Databases (Short Paper)

Authors: Arthur Jansen and Bart Kuijpers

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Space-time prisms provide a framework to model the uncertainty on the space-time points that a moving object may have visited between measured space-time locations, provided that a bound on the speed of the moving object is given. In this model, the alibi query asks whether two moving objects, given by their respective measured space-time locations and speed bound, may have met. An analytical solution to this problem was first given by Othman [Kuijpers et al., 2011]. In this paper, we address the generalised alibi query that asks the same question for an arbitrary number 𝗇 ≥ 2 of moving objects. We provide several solutions (mainly via the spatial and temporal projection) to this query with varying time complexities. These algorithmic solutions rely on techniques from convex and semi-algebraic geometry. We also address variants of the generalised alibi query where the question is asked for a given spatial location or a given moment in time.
Cite as

Arthur Jansen and Bart Kuijpers. Solutions to the Generalised Alibi Query in Moving Object Databases (Short Paper). In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 16:1-16:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.TIME.2025.16,
  author =	{Jansen, Arthur and Kuijpers, Bart},
  title =	{{Solutions to the Generalised Alibi Query in Moving Object Databases}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{16:1--16:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.16},
  URN =		{urn:nbn:de:0030-drops-244622},
  doi =		{10.4230/LIPIcs.TIME.2025.16},
  annote =	{Keywords: Convex geometry, Semi-algebraic geometry, Space-time prism, Geographic information systems, Quantifier elimination}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.TIME.2025.17
Visit Probability in Space-Time Prisms for Moving Object Data (Short Paper)

Authors: Arthur Jansen and Bart Kuijpers

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Space-time prisms have been extensively studied as a model to describe the uncertainty of the spatio-temporal location of a moving object in between measured space-time locations. In many applications, the desire has been expressed to provide an internal structure to these prisms, that includes what has been called "visit probability". Although several proposals have been studied in the past decades, a precise definition of this concept has been missing. The contribution of this paper is to provide such a specification by means of a formal framework for visit probability. Once this concept is established, we are able to derive on which parts of a prism, visit probability can be seen to give rise to a probability space.
Cite as

Arthur Jansen and Bart Kuijpers. Visit Probability in Space-Time Prisms for Moving Object Data (Short Paper). In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 17:1-17:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.TIME.2025.17,
  author =	{Jansen, Arthur and Kuijpers, Bart},
  title =	{{Visit Probability in Space-Time Prisms for Moving Object Data}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{17:1--17:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.17},
  URN =		{urn:nbn:de:0030-drops-244633},
  doi =		{10.4230/LIPIcs.TIME.2025.17},
  annote =	{Keywords: Spatio-temporal databases, moving object databases, space-time prisms, probability spaces}
}
Document
DOI: 10.4230/DagRep.2.8.16
Mobility Data Mining and Privacy (Dagstuhl Seminar 12331)

Authors: Christopher W. Clifton, Bart Kuijpers, Katharina Morik, and Yucel Saygin

Published in: Dagstuhl Reports, Volume 2, Issue 8 (2013)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 12331 "Mobility Data Mining and Privacy". Mobility data mining aims to extract knowledge from movement behaviour of people, but this data also poses novel privacy risks. This seminar gathered a multidisciplinary team for a conversation on how to balance the value in mining mobility data with privacy issues. The seminar focused on four key issues: Privacy in vehicular data, in cellular data, context-dependent privacy, and use of location uncertainty to provide privacy.
Cite as

Christopher W. Clifton, Bart Kuijpers, Katharina Morik, and Yucel Saygin. Mobility Data Mining and Privacy (Dagstuhl Seminar 12331). In Dagstuhl Reports, Volume 2, Issue 8, pp. 16-53, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@Article{clifton_et_al:DagRep.2.8.16,
  author =	{Clifton, Christopher W. and Kuijpers, Bart and Morik, Katharina and Saygin, Yucel},
  title =	{{Mobility Data Mining and Privacy (Dagstuhl Seminar 12331)}},
  pages =	{16--53},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2012},
  volume =	{2},
  number =	{8},
  editor =	{Clifton, Christopher W. and Kuijpers, Bart and Morik, Katharina and Saygin, Yucel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.8.16},
  URN =		{urn:nbn:de:0030-drops-37822},
  doi =		{10.4230/DagRep.2.8.16},
  annote =	{Keywords: Privacy, Mobility, Cellular, Vehicular Data}
}
Document
DOI: 10.4230/DagSemProc.08471.1
08471 Report – Geographic Privacy-Aware Knowledge Discovery and Delivery

Authors: Bart Kuijpers, Dino Pedreschi, Yucel Saygin, and Stefano Spaccapietra

Published in: Dagstuhl Seminar Proceedings, Volume 8471, Geographic Privacy-Aware Knowledge Discovery and Delivery (2009)

Abstract
The Dagstuhl-Seminar on Geographic Privacy-Aware Knowledge Discovery and Delivery was held during 16 - 21 November, 2008, with 37 participants registered from various countries from Europe, as well as other parts of the world such as United States, Canada, Argentina, and Brazil. Issues in the newly emerging area of geographic knowledge discovery with a privacy perspective were discussed in a week to consolidate some of the research questions. The Dagstuhl program included plenary sessions and special interest group meetings which continued even late in the evening with heated discussions. The plenary sessions were dedicated for the talks of some of the participants covering a variety of issues in geographic knowledge discovery and delivery. The reports on special interest group meetings (SIG) were also presented and discussed during the plenary sessions.
Cite as

Bart Kuijpers, Dino Pedreschi, Yucel Saygin, and Stefano Spaccapietra. 08471 Report – Geographic Privacy-Aware Knowledge Discovery and Delivery. In Geographic Privacy-Aware Knowledge Discovery and Delivery. Dagstuhl Seminar Proceedings, Volume 8471, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kuijpers_et_al:DagSemProc.08471.1,
  author =	{Kuijpers, Bart and Pedreschi, Dino and Saygin, Yucel and Spaccapietra, Stefano},
  title =	{{08471 Report – Geographic Privacy-Aware Knowledge Discovery and Delivery}},
  booktitle =	{Geographic Privacy-Aware Knowledge Discovery and Delivery},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8471},
  editor =	{Bart Kuijpers and Dino Pedreschi and Yucel Saygin and Stefano Spaccapietra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08471.1},
  URN =		{urn:nbn:de:0030-drops-20102},
  doi =		{10.4230/DagSemProc.08471.1},
  annote =	{Keywords: Spatio-temporal databases, data mining, privacy-preserving mining, data visualization}
}
Document
DOI: 10.4230/DagSemProc.08471.2
Propagating and measuring anchor uncertainty in space-time prisms on road networks

Authors: Bart Kuijpers, Harvey J. Miller, Tijs Neutens, and Walied Othman

Published in: Dagstuhl Seminar Proceedings, Volume 8471, Geographic Privacy-Aware Knowledge Discovery and Delivery (2009)

Abstract
Space-time prisms capture all possible spatio-temporal locations of a moving object between sample points given speed limit constraints on its movement. These sample points are usually considered to be perfect measurements. In this paper we restrict ourselves to a road network and extend the notion of sample points to sample regions, which are bounded, sometimes disconnected, subsets of space-time wherein each point is a possible location, with its respective probability, where a moving object could have originated from or arrived in. This model allows us to model measurement errors, multiple possible simultaneous locations and even flexibility of a moving object. We develop an algorithm that computes the envelope of all space-time prisms that have an anchor in these sample regions and we developed an algorithm that computes for any spatio-temporal point the probability with which a space-time prism, with anchors in these sample regions, contains that point. We implemented these algorithms in Mathematica to visualise all these newly-introduced concepts.
Cite as

Bart Kuijpers, Harvey J. Miller, Tijs Neutens, and Walied Othman. Propagating and measuring anchor uncertainty in space-time prisms on road networks. In Geographic Privacy-Aware Knowledge Discovery and Delivery. Dagstuhl Seminar Proceedings, Volume 8471, pp. 1-35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kuijpers_et_al:DagSemProc.08471.2,
  author =	{Kuijpers, Bart and Miller, Harvey J. and Neutens, Tijs and Othman, Walied},
  title =	{{Propagating and measuring anchor uncertainty in space-time prisms on road networks}},
  booktitle =	{Geographic Privacy-Aware Knowledge Discovery and Delivery},
  pages =	{1--35},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8471},
  editor =	{Bart Kuijpers and Dino Pedreschi and Yucel Saygin and Stefano Spaccapietra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08471.2},
  URN =		{urn:nbn:de:0030-drops-20072},
  doi =		{10.4230/DagSemProc.08471.2},
  annote =	{Keywords: Space-time prisms, beads, prisms, uncertainty, flexibility, time-geography}
}
Document
DOI: 10.4230/DagSemProc.08471.4
Temporal Support of Regular Expressions in Sequential Pattern Mining

Authors: Alejandro Vaisman, Leticia I. Gómez, and Bart Kuijpers

Published in: Dagstuhl Seminar Proceedings, Volume 8471, Geographic Privacy-Aware Knowledge Discovery and Delivery (2009)

Abstract
Classic algorithms for sequential pattern discovery,return all frequent sequences present in a database. Since, in general, only a few ones are interesting from a user's point of view, languages based on regular expressions (RE) have been proposed to restrict frequent sequences to the ones that satisfy user-specified constraints. Although the support of a sequence is computed as the number of data-sequences satisfying a pattern with respect to the total number of data-sequences in the database, once regular expressions come into play, new approaches to the concept of support are needed. For example, users may be interested in computing the support of the RE as a whole, in addition to the one of a particular pattern. As a simple example, the expression $(A|B).C$ is satisfied by sequences like A.C or B.C. Even though the semantics of this RE suggests that both of them are equally interesting to the user, if neither of them verifies a minimum support although together they do), they would not be retrieved. Also, when the items are frequently updated, the traditional way of counting support in sequential pattern mining may lead to incorrect (or, at least incomplete), conclusions. For example, if we are looking for the support of the sequence A.B, where A and B are two items such that A was created after B, all sequences in the database that were completed before A was created, can never produce a match. Therefore, accounting for them would underestimate the support of the sequence A.B. The problem gets more involved if we are interested in categorical sequential patterns. In light of the above, in this paper we propose to revise the classic notion of support in sequential pattern mining, introducing the concept of temporal support of regular expressions, intuitively defined as the number of sequences satisfying a target pattern, out of the total number of sequences that could have possibly matched such pattern, where the pattern is defined as a RE over complex items (i.e., not only item identifiers, but also attributes and functions). We present and discuss a theoretical framework for these novel notion of support.
Cite as

Alejandro Vaisman, Leticia I. Gómez, and Bart Kuijpers. Temporal Support of Regular Expressions in Sequential Pattern Mining. In Geographic Privacy-Aware Knowledge Discovery and Delivery. Dagstuhl Seminar Proceedings, Volume 8471, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{vaisman_et_al:DagSemProc.08471.4,
  author =	{Vaisman, Alejandro and G\'{o}mez, Leticia I. and Kuijpers, Bart},
  title =	{{Temporal Support of Regular Expressions in Sequential Pattern Mining}},
  booktitle =	{Geographic Privacy-Aware Knowledge Discovery and Delivery},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8471},
  editor =	{Bart Kuijpers and Dino Pedreschi and Yucel Saygin and Stefano Spaccapietra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08471.4},
  URN =		{urn:nbn:de:0030-drops-20087},
  doi =		{10.4230/DagSemProc.08471.4},
  annote =	{Keywords: Temporal support, sequential pattern mining}
}
Document
DOI: 10.4230/DagSemProc.07212.1
07212 Abstracts Collection – Constraint Databases, Geometric Elimination ang Geographic Information Systems

Authors: Bernd Bank, Max J. Egenhofer, and Bart Kuijpers

Published in: Dagstuhl Seminar Proceedings, Volume 7212, Constraint Databases, Geometric Elimination and Geographic Information Systems (2007)

Abstract
From 20.05. to 25.05., the Dagstuhl Seminar 07212 ``Constraint Databases, Geometric Elimination and Geographic Information Systems'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Bernd Bank, Max J. Egenhofer, and Bart Kuijpers. 07212 Abstracts Collection – Constraint Databases, Geometric Elimination ang Geographic Information Systems. In Constraint Databases, Geometric Elimination and Geographic Information Systems. Dagstuhl Seminar Proceedings, Volume 7212, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{bank_et_al:DagSemProc.07212.1,
  author =	{Bank, Bernd and Egenhofer, Max J. and Kuijpers, Bart},
  title =	{{07212 Abstracts Collection – Constraint Databases, Geometric Elimination ang Geographic Information Systems}},
  booktitle =	{Constraint Databases, Geometric Elimination and Geographic Information Systems},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7212},
  editor =	{Bernd Bank and Max J. Egenhofer and Bart Kuijpers},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07212.1},
  URN =		{urn:nbn:de:0030-drops-12870},
  doi =		{10.4230/DagSemProc.07212.1},
  annote =	{Keywords: Constraint databases, geometric elimination, quantier elimination algorithms, geographic information systems}
}
Document
DOI: 10.4230/DagSemProc.07212.2
07212 Manifesto – Constraint Databases, Geometric Elimination ang Geographic Information Systems

Authors: Bernd Bank, Max J. Egenhofer, Joos Heintz, Bart Kuijpers, and Peter Revesz

Published in: Dagstuhl Seminar Proceedings, Volume 7212, Constraint Databases, Geometric Elimination and Geographic Information Systems (2007)

Abstract
During the last two decades the topic of constraint databases has evolved into a mature area of computer science with sound mathematical foundations and with a profound theoretical understanding of the expressive power of a variety of query languages. Constraint databases are especially suited for applications in which possibly infinite sets of continuous data, that have a geometric interpretation, need to be stored in a computer. Today, the most important application domains of constraint databases are geographic information systems (GIS), spatial databases and spatio-temporal databases. In these applications infinite geometrical sets of continuous data are finitely represented by means of finite combinations of polynomial equality and inequality constraints that describe these data sets (in mathematical terms these geometrical data sets are known as semi-algebraic sets and they have been extensively studied in real algebraic geometry). On the other hand, constraint databases provide us with a new view on classic (linear and nonlinear) optimization theory.
Cite as

Bernd Bank, Max J. Egenhofer, Joos Heintz, Bart Kuijpers, and Peter Revesz. 07212 Manifesto – Constraint Databases, Geometric Elimination ang Geographic Information Systems. In Constraint Databases, Geometric Elimination and Geographic Information Systems. Dagstuhl Seminar Proceedings, Volume 7212, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{bank_et_al:DagSemProc.07212.2,
  author =	{Bank, Bernd and Egenhofer, Max J. and Heintz, Joos and Kuijpers, Bart and Revesz, Peter},
  title =	{{07212 Manifesto – Constraint Databases, Geometric Elimination ang Geographic Information Systems}},
  booktitle =	{Constraint Databases, Geometric Elimination and Geographic Information Systems},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7212},
  editor =	{Bernd Bank and Max J. Egenhofer and Bart Kuijpers},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07212.2},
  URN =		{urn:nbn:de:0030-drops-12824},
  doi =		{10.4230/DagSemProc.07212.2},
  annote =	{Keywords: Constraint databases, elimination procedures, geographical information systems}
}
Document
DOI: 10.4230/DagSemProc.07212.4
An analytic solution to the alibi query in the bead model for moving object data

Authors: Bart Kuijpers and Walied Othman

Published in: Dagstuhl Seminar Proceedings, Volume 7212, Constraint Databases, Geometric Elimination and Geographic Information Systems (2007)

Abstract
Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When also speed limitations in these sample points are known, beads can be used to model the uncertainty about the object's location in between sample points. In this setting, a query of particular interest, that has been studied in the literature of geographic information systems (GIS), is the alibi query. This boolean query asks whether two moving objects can have physically met. This adds up to deciding whether the necklaces of beads of these objects intersect. This problem can be reduced to deciding whether two beads intersect. Since, existing software to solve this problem fails to answer this question within a reasonable time, we propose an analytical solution to the alibi query, which can be used to answer the alibi query in constant time, a matter of milliseconds or less, for two single beads and in time proportional to the product of their lengths for necklaces of beads.
Cite as

Bart Kuijpers and Walied Othman. An analytic solution to the alibi query in the bead model for moving object data. In Constraint Databases, Geometric Elimination and Geographic Information Systems. Dagstuhl Seminar Proceedings, Volume 7212, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{kuijpers_et_al:DagSemProc.07212.4,
  author =	{Kuijpers, Bart and Othman, Walied},
  title =	{{An analytic solution to the alibi query in the bead model for moving object data}},
  booktitle =	{Constraint Databases, Geometric Elimination and Geographic Information Systems},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7212},
  editor =	{Bernd Bank and Max J. Egenhofer and Bart Kuijpers},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07212.4},
  URN =		{urn:nbn:de:0030-drops-12864},
  doi =		{10.4230/DagSemProc.07212.4},
  annote =	{Keywords: Beads, uncertainty, alibi, query, solution, quantifier elimination, constraint database}
}
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