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Combinatorial generation via permutation languages. V. Acyclic orientations
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Cardinal, Jean, Hoang, Hung, Merino, Arturo, Micka, Ondrej and Mutze, Torsten (2023) Combinatorial generation via permutation languages. V. Acyclic orientations. SIAM Journal on Discrete Mathematics, 37 (3). pp. 1509-1547. doi:10.1137/23M1546567 ISSN 0895-4801.
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Official URL: http://doi.org/10.1137/23M1546567
Abstract
In 1993, Savage, Squire, and West described an inductive construction for generating every acyclic orientation of a chordal graph exactly once, flipping one arc at a time. We provide two generalizations of this result. Firstly, we describe Gray codes for acyclic orientations of hypergraphs that satisfy a simple ordering condition, which generalizes the notion of perfect elimination order of graphs. This unifies the Savage-Squire-West construction with a recent algorithm for generating elimination trees of chordal graphs. Secondly, we consider quotients of lattices of acyclic orientations of chordal graphs, and we provide a Gray code for them, addressing a question raised by Pilaud. This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group. Our algorithms are derived from the Hartung-Hoang-M\"utze-Williams combinatorial generation framework, and they yield simple algorithms for computing Hamilton paths and cycles on large classes of polytopes, including chordal nestohedra and quotientopes. In particular, we derive an efficient implementation of the Savage-Squire-West construction. Along the way, we give an overview of old and recent results about the polyhedral and order-theoretic aspects of acyclic orientations of graphs and hypergraphs.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Journal or Publication Title: | SIAM Journal on Discrete Mathematics | ||||
Publisher: | Society for Industrial and Applied Mathematics | ||||
ISSN: | 0895-4801 | ||||
Official Date: | 10 March 2023 | ||||
Dates: |
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Volume: | 37 | ||||
Number: | 3 | ||||
Page Range: | pp. 1509-1547 | ||||
DOI: | 10.1137/23M1546567 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Reuse Statement (publisher, data, author rights): | First Published in SIAM Journal on Discrete Mathematics in 37(3), pp. 1509-1547. published by the Society for Industrial and Applied Mathematics (SIAM) © by SIAM. Unauthorized reproduction of this article is prohibited. | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 13 March 2023 | ||||
Date of first compliant Open Access: | 25 July 2023 | ||||
Related URLs: | |||||
Open Access Version: |
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