COMBINATORIAL GENERATION VIA PERMUTATION LANGUAGES. V. ACYCLIC ORIENTATIONS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

COMBINATORIAL GENERATION VIA PERMUTATION LANGUAGES. V. ACYCLIC ORIENTATIONS

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. 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&quot;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.

Název v anglickém jazyce

COMBINATORIAL GENERATION VIA PERMUTATION LANGUAGES. V. ACYCLIC ORIENTATIONS

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. 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&quot;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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 periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Svazek periodika

37

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

1509-1547

Kód UT WoS článku

001042702500007

EID výsledku v databázi Scopus

2-s2.0-85167601352