Zigzagging through acyclic orientations of chordal graphs and hypergraphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10476041" target="_blank" >RIV/00216208:11320/23:10476041 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/1.9781611977554.ch117" target="_blank" >https://doi.org/10.1137/1.9781611977554.ch117</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/1.9781611977554.ch117" target="_blank" >10.1137/1.9781611977554.ch117</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Zigzagging through acyclic orientations of chordal graphs and hypergraphs

Popis výsledku v původním jazyce

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 (SODA 2022). 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 (FPSAC 2022). This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group (SODA 2020). Our algorithms are derived from the Hartung-Hoang-Mütze-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.

Název v anglickém jazyce

Zigzagging through acyclic orientations of chordal graphs and hypergraphs

Popis výsledku anglicky

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 (SODA 2022). 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 (FPSAC 2022). This also generalizes a recent algorithm for generating lattice congruences of the weak order on the symmetric group (SODA 2020). Our algorithms are derived from the Hartung-Hoang-Mütze-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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA22-15272S" target="_blank" >GA22-15272S: Principy kombinatorického generování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ISBN

978-1-61197-755-4

ISSN

—

e-ISSN

—

Počet stran výsledku

14

Strana od-do

3029-3042

Název nakladatele

Society for Industrial and Applied Mathematics

Místo vydání

Philadelphia, USA

Místo konání akce

Florenc, Italy

Datum konání akce

22. 1. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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