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A fast algorithm to generate open meandric systems and meanders

Published: 06 April 2010 Publication History

Abstract

An open meandric system is a planar configuration of acyclic curves crossing an infinite horizontal line in the plane such that the curves may extend in both horizontal directions. We present a fast, recursive algorithm to exhaustively generate open meandric systems with n crossings. We then illustrate how to modify the algorithm to generate unidirectional open meandric systems (the curves extend only to the right) and nonisomorphic open meandric systems where equivalence is taken under horizontal reflection. Each algorithm can be modified to generate systems with exactly k curves. In the unidirectional case when k = 1, we can apply a minor modification along with some additional optimization steps to yield the first fast and simple algorithm to generate open meanders.

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  • (2025)Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meandersTheoretical Computer Science10.1016/j.tcs.2024.115053(115053)Online publication date: Jan-2025
  • (2024)Meanders: A personal perspective to the memory of Pierre RosenstiehlEuropean Journal of Combinatorics10.1016/j.ejc.2023.103817119(103817)Online publication date: Jun-2024
  • (2023)Generating Cyclic Rotation Gray Codes for Stamp Foldings and Semi-meandersCombinatorial Algorithms10.1007/978-3-031-34347-6_23(271-281)Online publication date: 7-Jun-2023

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  1. A fast algorithm to generate open meandric systems and meanders

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    cover image ACM Transactions on Algorithms
    ACM Transactions on Algorithms  Volume 6, Issue 2
    March 2010
    373 pages
    ISSN:1549-6325
    EISSN:1549-6333
    DOI:10.1145/1721837
    Issue’s Table of Contents
    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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    Publication History

    Published: 06 April 2010
    Accepted: 01 December 2008
    Revised: 01 December 2008
    Received: 01 June 2007
    Published in TALG Volume 6, Issue 2

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    Author Tags

    1. CAT algorithm
    2. meander
    3. open meandric system

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    • (2025)Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meandersTheoretical Computer Science10.1016/j.tcs.2024.115053(115053)Online publication date: Jan-2025
    • (2024)Meanders: A personal perspective to the memory of Pierre RosenstiehlEuropean Journal of Combinatorics10.1016/j.ejc.2023.103817119(103817)Online publication date: Jun-2024
    • (2023)Generating Cyclic Rotation Gray Codes for Stamp Foldings and Semi-meandersCombinatorial Algorithms10.1007/978-3-031-34347-6_23(271-281)Online publication date: 7-Jun-2023

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