3 Search Results for "Jones, Timothy M."

Document
DOI: 10.4230/LIPIcs.TIME.2019.20
On Verifying Timed Hyperproperties

Authors: Hsi-Ming Ho, Ruoyu Zhou, and Timothy M. Jones

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)

Abstract
We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMTL, a timed extension of HyperLTL. Depending on whether interleaving of events in different traces is allowed, two possible semantics can be defined for timed hyperproperties: synchronous and asynchronous. While the satisfiability problem can be decided similarly as for HyperLTL regardless of the choice of semantics, we show that the model-checking problem for HyperMTL, unless the specification is alternation-free, is undecidable even when very restricted timing constraints are allowed. On the positive side, we show that model checking HyperMTL with quantifier alternations is possible under certain conditions in the synchronous semantics, or when there is a fixed bound on the length of the time domain.
Cite as

Hsi-Ming Ho, Ruoyu Zhou, and Timothy M. Jones. On Verifying Timed Hyperproperties. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ho_et_al:LIPIcs.TIME.2019.20,
  author =	{Ho, Hsi-Ming and Zhou, Ruoyu and Jones, Timothy M.},
  title =	{{On Verifying Timed Hyperproperties}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.20},
  URN =		{urn:nbn:de:0030-drops-113782},
  doi =		{10.4230/LIPIcs.TIME.2019.20},
  annote =	{Keywords: Timed Automata, Temporal Logics, Cybersecurity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.24
Dynamic Geometric Data Structures via Shallow Cuttings

Authors: Timothy M. Chan

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
We present new results on a number of fundamental problems about dynamic geometric data structures: 1) We describe the first fully dynamic data structures with sublinear amortized update time for maintaining (i) the number of vertices or the volume of the convex hull of a 3D point set, (ii) the largest empty circle for a 2D point set, (iii) the Hausdorff distance between two 2D point sets, (iv) the discrete 1-center of a 2D point set, (v) the number of maximal (i.e., skyline) points in a 3D point set. The update times are near n^{11/12} for (i) and (ii), n^{7/8} for (iii) and (iv), and n^{2/3} for (v). Previously, sublinear bounds were known only for restricted "semi-online" settings [Chan, SODA 2002]. 2) We slightly improve previous fully dynamic data structures for answering extreme point queries for the convex hull of a 3D point set and nearest neighbor search for a 2D point set. The query time is O(log^2n), and the amortized update time is O(log^4n) instead of O(log^5n) [Chan, SODA 2006; Kaplan et al., SODA 2017]. 3) We also improve previous fully dynamic data structures for maintaining the bichromatic closest pair between two 2D point sets and the diameter of a 2D point set. The amortized update time is O(log^4n) instead of O(log^7n) [Eppstein 1995; Chan, SODA 2006; Kaplan et al., SODA 2017].
Cite as

Timothy M. Chan. Dynamic Geometric Data Structures via Shallow Cuttings. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chan:LIPIcs.SoCG.2019.24,
  author =	{Chan, Timothy M.},
  title =	{{Dynamic Geometric Data Structures via Shallow Cuttings}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.24},
  URN =		{urn:nbn:de:0030-drops-104288},
  doi =		{10.4230/LIPIcs.SoCG.2019.24},
  annote =	{Keywords: dynamic data structures, convex hulls, nearest neighbor search, closest pair, shallow cuttings}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.21
On Locality-Sensitive Orderings and Their Applications

Authors: Timothy M. Chan, Sariel Har-Peled, and Mitchell Jones

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
For any constant d and parameter epsilon > 0, we show the existence of (roughly) 1/epsilon^d orderings on the unit cube [0,1)^d, such that any two points p, q in [0,1)^d that are close together under the Euclidean metric are "close together" in one of these linear orderings in the following sense: the only points that could lie between p and q in the ordering are points with Euclidean distance at most epsilon | p - q | from p or q. These orderings are extensions of the Z-order, and they can be efficiently computed. Functionally, the orderings can be thought of as a replacement to quadtrees and related structures (like well-separated pair decompositions). We use such orderings to obtain surprisingly simple algorithms for a number of basic problems in low-dimensional computational geometry, including (i) dynamic approximate bichromatic closest pair, (ii) dynamic spanners, (iii) dynamic approximate minimum spanning trees, (iv) static and dynamic fault-tolerant spanners, and (v) approximate nearest neighbor search.
Cite as

Timothy M. Chan, Sariel Har-Peled, and Mitchell Jones. On Locality-Sensitive Orderings and Their Applications. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chan_et_al:LIPIcs.ITCS.2019.21,
  author =	{Chan, Timothy M. and Har-Peled, Sariel and Jones, Mitchell},
  title =	{{On Locality-Sensitive Orderings and Their Applications}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.21},
  URN =		{urn:nbn:de:0030-drops-101140},
  doi =		{10.4230/LIPIcs.ITCS.2019.21},
  annote =	{Keywords: Approximation algorithms, Data structures, Computational geometry}
}
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