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Detection is easier than computation (Extended Abstract)

Authors:

Bernard Chazelle,

David P. DobkinAuthors Info & Claims

STOC '80: Proceedings of the twelfth annual ACM symposium on Theory of computing

Pages 146 - 153

https://doi.org/10.1145/800141.804662

Published: 28 April 1980 Publication History

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Abstract

Perhaps the most important application of computer geometry involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation where the objects are given as input and their intersection is returned as output. However, for many applications, we may assume that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint. For this problem, none of the previous lower bounds are valid and we propose algorithms requiring sublinear time for their solution in 2 and 3 dimensions.

References

[1]

Bentley, J. and Ottmann,Th., Algorithms for reporting and counting geometric intersections, Carnegie-Mellon University, August 1978.

Google Scholar

[2]

Forrest, A.R., Private communication to David Dobkin, March 29, 1979.

Google Scholar

[3]

Kiefer, J., Sequential Minimax Search for a Maximum, Proc. Amer. Math. Soc. 4 (1953), 502–506.

Google Scholar

[4]

Muller, D. and Preparata, F., Finding the intersection of 2 convex polyhedra, Tech. Report Univ. of Illinois, Urbana, Ill., Oct. 1977.

Google Scholar

[5]

Newman, W. and Sproull, R., Principles of Interactive Computer Graphics, second edition, McGraw Hill, New York, 1979.

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Google Scholar

[6]

Shamos, M., Geometric Complexity, Proc. Seventh Annual ACM Symp. on Theory of Comput. (1975), 224–233.

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Google Scholar

[7]

Shamos, M. and Hoey, D., Geometric Intersection Problems, Proc. of the 17th Annual Symp. on Found. of Comp. Sci. (1976), 208–215.

Google Scholar

[8]

Tomlin, D., private communication to David Dobkin.

Google Scholar

Cited By

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Johnson J(2018)On the relationship between dynamics and complexity in multi-agent collision avoidanceAutonomous Robots10.1007/s10514-018-9743-442:7(1389-1404)Online publication date: 23-Apr-2018
https://doi.org/10.1007/s10514-018-9743-4
Barba LLangerman SIndyk P(2015)Optimal detection of intersections between convex polyhedraProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722238(1641-1654)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722238
Van Hoesel LTüYsüZ Erman ADilo AHavinga P(2013)Geo-casting of queries combined with coverage area reporting for wireless sensor networksAd Hoc Networks10.1016/j.adhoc.2012.04.01011:1(104-123)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1016/j.adhoc.2012.04.010
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Index Terms

Detection is easier than computation (Extended Abstract)
1. Theory of computation

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STOC '80: Proceedings of the twelfth annual ACM symposium on Theory of computing

April 1980

446 pages

ISBN:0897910176

DOI:10.1145/800141

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 28 April 1980

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STOC '80 Paper Acceptance Rate 47 of 125 submissions, 38%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Johnson J(2018)On the relationship between dynamics and complexity in multi-agent collision avoidanceAutonomous Robots10.1007/s10514-018-9743-442:7(1389-1404)Online publication date: 23-Apr-2018
https://doi.org/10.1007/s10514-018-9743-4
Barba LLangerman SIndyk P(2015)Optimal detection of intersections between convex polyhedraProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722238(1641-1654)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722238
Van Hoesel LTüYsüZ Erman ADilo AHavinga P(2013)Geo-casting of queries combined with coverage area reporting for wireless sensor networksAd Hoc Networks10.1016/j.adhoc.2012.04.01011:1(104-123)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1016/j.adhoc.2012.04.010
Erman ADilo AHoesel LHavinga P(2011)On Mobility Management in Multi-Sink Sensor Networks for Geocasting of QueriesSensors10.3390/s11121141511:12(11415-11446)Online publication date: 1-Dec-2011
https://doi.org/10.3390/s111211415
Dobkin DKirkpatrick D(2005)Fast detection of polyhedral intersectionsAutomata, Languages and Programming10.1007/BFb0012765(154-165)Online publication date: 22-Oct-2005
https://doi.org/10.1007/BFb0012765
Stifter S(2005)Predictions about collision free paths from intersection testsComputational Geometry-Methods, Algorithms and Applications10.1007/3-540-54891-2_23(309-320)Online publication date: 29-May-2005
https://doi.org/10.1007/3-540-54891-2_23
Bhattacharya BToussaint G(2005)Computing shortest transversalsAutomata, Languages and Programming10.1007/3-540-54233-7_171(649-660)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-54233-7_171
Stifter S(2005)A generalization of the roider method to solve the robot collision problem in 3DSymbolic and Algebraic Computation10.1007/3-540-51084-2_32(332-343)Online publication date: 27-May-2005
https://doi.org/10.1007/3-540-51084-2_32
Reichling M(2005)On the detection of a common intersection of κ convex polyhedraComputational Geometry and its Applications10.1007/3-540-50335-8_34(180-186)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-50335-8_34
Ghosh S(2005)A linear-time algorithm for determining the intersection type of two star polygonsFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-13883-8_80(317-330)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-13883-8_80
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Query point visibility computation in polygons with holes

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