research-article

Competitive query strategies for minimising the ply of the potential locations of moving points

Authors:

David Kirkpatrick,

Maarten Löffler,

Frank StaalsAuthors Info & Claims

SoCG '13: Proceedings of the twenty-ninth annual symposium on Computational geometry

Pages 155 - 164

https://doi.org/10.1145/2462356.2462395

Published: 17 June 2013 Publication History

Abstract

We study the problem of maintaining the locations of a collection of n entities that are moving with some fixed upper bound on their speed. We assume a setting where we may query the current location of entities, but handling this query takes a certain unit of time, during which we cannot query any other entities. In this model, we can never know the exact locations of all entities at any one time. Instead, we maintain a representation of the potential locations of all entities. We measure the quality of this representation by its ply: the maximum over all points p of the number of entities that could potentially be at p.

Since the ply could be large for every query strategy, we analyse the performance of our algorithms in a competitive framework: we consider the worst case ratio of the ply achieved by our algorithms to the intrinsic ply (the smallest ply achievable by any algorithm, even one that knows in advance the full trajectories of all entities). We show that, if our goal is to mimimise the ply at some number τ of time units in the future, an O(1)-competitive algorithm exists, provided τ is sufficiently large. If τ is small and the n entities move in any constant dimension d, our algorithm is O((l/τ + 1)^d-d/(d+1))-competitive, where l is the median of the lengths of time since the $n$ entity locations were last known precisely.

We also provide matching lower bounds, and we show that computing the intrinsic ply exactly is NP-hard, even when the trajectories are known in advance.

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Cited By

Evans WTabatabaee S(2024)Minimizing the Size of the Uncertainty Regions for Centers of Moving EntitiesLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_18(273-287)Online publication date: 6-Mar-2024
https://doi.org/10.1007/978-3-031-55598-5_18
Buchin KFan CLöffler MPopov ARaichel BRoeloffzen M(2023)Fréchet Distance for Uncertain CurvesACM Transactions on Algorithms10.1145/359764019:3(1-47)Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1145/3597640
Evans WKirkpatrick D(2023)Minimizing Query Frequency to Bound Congestion Potential for Moving Entities at a Fixed Target TimeFundamentals of Computation Theory10.1007/978-3-031-43587-4_12(162-175)Online publication date: 21-Sep-2023
https://doi.org/10.1007/978-3-031-43587-4_12
Show More Cited By

Index Terms

Competitive query strategies for minimising the ply of the potential locations of moving points
1. Theory of computation

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cover image ACM Conferences

SoCG '13: Proceedings of the twenty-ninth annual symposium on Computational geometry

June 2013

472 pages

ISBN:9781450320313

DOI:10.1145/2462356

General Chairs:
Guilherme D. da Fonseca
UNIRIO
,
Thomas Lewiner
PUC-Rio
,
Luis Peñaranda
IMPA
,
Program Chairs:
Timothy Chan
University of Waterloo
,
Rolf Klein
University of Bonn

Copyright © 2013 ACM.

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Published: 17 June 2013

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SoCG '13: Symposium on Computational Geometry 2013

June 17 - 20, 2013

Rio de Janeiro, Brazil

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SoCG '13 Paper Acceptance Rate 48 of 137 submissions, 35%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Evans WTabatabaee S(2024)Minimizing the Size of the Uncertainty Regions for Centers of Moving EntitiesLATIN 2024: Theoretical Informatics10.1007/978-3-031-55598-5_18(273-287)Online publication date: 6-Mar-2024
https://doi.org/10.1007/978-3-031-55598-5_18
Buchin KFan CLöffler MPopov ARaichel BRoeloffzen M(2023)Fréchet Distance for Uncertain CurvesACM Transactions on Algorithms10.1145/359764019:3(1-47)Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1145/3597640
Evans WKirkpatrick D(2023)Minimizing Query Frequency to Bound Congestion Potential for Moving Entities at a Fixed Target TimeFundamentals of Computation Theory10.1007/978-3-031-43587-4_12(162-175)Online publication date: 21-Sep-2023
https://doi.org/10.1007/978-3-031-43587-4_12
Busto DEvans WKirkpatrick DChan T(2019)Minimizing interference potential among moving entitiesProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310582(2400-2418)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310582

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