COMBINATORIAL GENERATION VIA PERMUTATION LANGUAGES. V. ACYCLIC ORIENTATIONS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10467256" target="_blank" >RIV/00216208:11320/23:10467256 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=exvhY1Gclk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=exvhY1Gclk</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/23M1546567" target="_blank" >10.1137/23M1546567</a>
Alternative languages
Result language
angličtina
Original language name
COMBINATORIAL GENERATION VIA PERMUTATION LANGUAGES. V. ACYCLIC ORIENTATIONS
Original language description
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. First, 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. Second, 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--Mu"tze--Williams combina-torial 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA22-15272S" target="_blank" >GA22-15272S: Principles of combinatorial generation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
1095-7146
Volume of the periodical
37
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
39
Pages from-to
1509-1547
UT code for WoS article
001042702500007
EID of the result in the Scopus database
2-s2.0-85167601352