Zigzagging through acyclic orientations of chordal graphs and hypergraphs

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Zigzagging through acyclic orientations of chordal graphs and hypergraphs

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. 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.

Czech name

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Czech description

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Type

D - Article in proceedings

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)

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)

Publication year

2023

Confidentiality

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

Article name in the collection

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ISBN

978-1-61197-755-4

ISSN

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e-ISSN

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Number of pages

14

Pages from-to

3029-3042

Publisher name

Society for Industrial and Applied Mathematics

Place of publication

Philadelphia, USA

Event location

Florenc, Italy

Event date

Jan 22, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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