On 3SUM-hard Problems in the Decision Tree Model

Esther Ezra

doi:10.1007/978-3-030-80049-9_16

On 3SUM-hard Problems in the Decision Tree Model

Esther Ezra

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We describe subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets A, B, and C of points in the plane, that satisfy a pair of polynomial equations. In particular, this has an application to detect collinearity among three sets A, B, C of n points each, in the complex plane, when each of the sets A, B, C lies on some constant-degree algebraic curve. In another development, we present a subquadratic algorithm, in the algebraic decision-tree model, for the following problem: Given a pair of sets A, B each consisting of n pairwise disjoint line segments in the plane, and a third set C of arbitrary line segments in the plane, determine whether A× B× C contains a triple of concurrent segments. This is one of four 3sum-hard geometric problems recently studied by Chan (2020). The results reported in this extended abstract are based on the recent studies of the author with Aronov and Sharir (2020, 2021).

Original language	English
Title of host publication	Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings
Editors	Liesbeth De Mol, Andreas Weiermann, Florin Manea, David Fernández-Duque
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	178-188
Number of pages	11
ISBN (Print)	9783030800482
DOIs	https://doi.org/10.1007/978-3-030-80049-9_16
State	Published - 2021
Event	17th Conference on Computability in Europe, CiE 2021 - Virtual, Online Duration: 5 Jul 2021 → 9 Jul 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12813 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th Conference on Computability in Europe, CiE 2021
City	Virtual, Online
Period	5/07/21 → 9/07/21

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Funding

Work partially supported by NSF CAREER under grant CCF:AF-1553354 and by Grant 824/17 from the Israel Science Foundation.

Funders	Funder number
National Science Foundation	824/17, AF-1553354
Israel Science Foundation

Keywords

3SUM-hard problems
Algebraic decision tree model
Collinearity testing
Segment concurrency

Access to Document

10.1007/978-3-030-80049-9_16

Cite this

Ezra, E. (2021). On 3SUM-hard Problems in the Decision Tree Model. In L. De Mol, A. Weiermann, F. Manea, & D. Fernández-Duque (Eds.), Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings (pp. 178-188). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12813 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-80049-9_16

Ezra, Esther. / On 3SUM-hard Problems in the Decision Tree Model. Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings. editor / Liesbeth De Mol ; Andreas Weiermann ; Florin Manea ; David Fernández-Duque. Springer Science and Business Media Deutschland GmbH, 2021. pp. 178-188 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Ezra, E 2021, On 3SUM-hard Problems in the Decision Tree Model. in L De Mol, A Weiermann, F Manea & D Fernández-Duque (eds), Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12813 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 178-188, 17th Conference on Computability in Europe, CiE 2021, Virtual, Online, 5/07/21. https://doi.org/10.1007/978-3-030-80049-9_16

On 3SUM-hard Problems in the Decision Tree Model. / Ezra, Esther.
Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings. ed. / Liesbeth De Mol; Andreas Weiermann; Florin Manea; David Fernández-Duque. Springer Science and Business Media Deutschland GmbH, 2021. p. 178-188 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12813 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ezra E. On 3SUM-hard Problems in the Decision Tree Model. In De Mol L, Weiermann A, Manea F, Fernández-Duque D, editors, Connecting with Computability - 17th Conference on Computability in Europe, CiE 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 178-188. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-80049-9_16

On 3SUM-hard Problems in the Decision Tree Model

Abstract

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