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Coordinate representation of order types requires exponential storage

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B. SturmfelsAuthors Info & Claims

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

Pages 405 - 410

https://doi.org/10.1145/73007.73046

Published: 01 February 1989 Publication History

Abstract

We give doubly exponential upper and lower bounds on the size of the smallest grid on which we can embed every planar configuration of n points in general position up to order type. The lower bound is achieved by the construction of a widely dispersed “rigid” configuration which is then modified to one in general position by recent techniques of Sturmfels and White, while the upper bound uses recent results of Grigor'ev and Vorobjou on the solution of simultaneous inequalities. This provides a sharp answer to a question first posed by Chazelle.

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Cited By

Scheucher M(2022)Many Order Types on Integer Grids of Polynomial SizeComputational Geometry10.1016/j.comgeo.2022.101924(101924)Online publication date: Aug-2022
https://doi.org/10.1016/j.comgeo.2022.101924
Chiu MKorman MSuderland MTokuyama T(2022)Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital RaysDiscrete & Computational Geometry10.1007/s00454-021-00349-668:3(902-944)Online publication date: 15-Mar-2022
https://doi.org/10.1007/s00454-021-00349-6
Oropeza MTóth C(2021)Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning TreesInformation Processing Letters10.1016/j.ipl.2021.106116(106116)Online publication date: Mar-2021
https://doi.org/10.1016/j.ipl.2021.106116
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Index Terms

Coordinate representation of order types requires exponential storage
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory

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cover image ACM Conferences

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

February 1989

600 pages

ISBN:0897913078

DOI:10.1145/73007

Editor:
D. S. Johnson

Copyright © 1989 ACM.

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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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Published: 01 February 1989

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STOC89: 21st Annual ACM Symposium on the Theory of Computing

May 14 - 17, 1989

Washington, Seattle, USA

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STOC '89 Paper Acceptance Rate 56 of 196 submissions, 29%;

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

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Cited By

Scheucher M(2022)Many Order Types on Integer Grids of Polynomial SizeComputational Geometry10.1016/j.comgeo.2022.101924(101924)Online publication date: Aug-2022
https://doi.org/10.1016/j.comgeo.2022.101924
Chiu MKorman MSuderland MTokuyama T(2022)Distance Bounds for High Dimensional Consistent Digital Rays and 2-D Partially-Consistent Digital RaysDiscrete & Computational Geometry10.1007/s00454-021-00349-668:3(902-944)Online publication date: 15-Mar-2022
https://doi.org/10.1007/s00454-021-00349-6
Oropeza MTóth C(2021)Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning TreesInformation Processing Letters10.1016/j.ipl.2021.106116(106116)Online publication date: Mar-2021
https://doi.org/10.1016/j.ipl.2021.106116
Erickson Jvan der Hoog IMiltzow T(2020)Smoothing the gap between NP and ER2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00099(1022-1033)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00099
Caraballo LDíaz-Báñez JFabila-Monroy RHidalgo-Toscano CLeaños JMontejano A(2020)On the number of order types in integer grids of small sizeComputational Geometry10.1016/j.comgeo.2020.101730(101730)Online publication date: Nov-2020
https://doi.org/10.1016/j.comgeo.2020.101730
Çağırıcı OHliněný PPokrývka FSankaran A(2020)Clique-Width of Point ConfigurationsGraph-Theoretic Concepts in Computer Science10.1007/978-3-030-60440-0_5(54-66)Online publication date: 9-Oct-2020
https://doi.org/10.1007/978-3-030-60440-0_5
Han JKohayakawa YSales MStagni HChan T(2019)Extremal and probabilistic results for order typesProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310462(426-435)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310462
Kratsch SPhilip GRay S(2016)Point Line CoverACM Transactions on Algorithms10.1145/283291212:3(1-16)Online publication date: 25-Apr-2016
https://dl.acm.org/doi/10.1145/2832912
Cardinal J(2015)Computational Geometry Column 62ACM SIGACT News10.1145/2852040.285205346:4(69-78)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1145/2852040.2852053
Kratsch SPhilip GRay SChekuri C(2014)Point line coverProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634190(1596-1606)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634190
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