Asymptotic analysis and efficient random sampling of directed ordered acyclic graphs - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Asymptotic analysis and efficient random sampling of directed ordered acyclic graphs

Martin Pépin
Alfredo Viola
  • Fonction : Auteur
  • PersonId : 1376611

Résumé

Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample them uniformly at random has been solved respectively in the 70’s and the 00’s. In this paper, we propose to explore a new variation of this model where DAGs are endowed with an independent ordering of the out-edges of each vertex, thus allowing to model a wide range of existing data structures. We provide efficient algorithms for sampling objects of this new class, both with or without control on the number of edges, and obtain an asymptotic equivalent of their number. We also show the applicability of our method by providing an effective algorithm for the random generation of classical labelled DAGs with a prescribed number of vertices and edges, based on a similar approach. This is the first known algorithm for sampling labelled DAGs with full control on the number of edges, and it meets a need in terms of applications, that had already been acknowledged in the literature.
Fichier principal
Vignette du fichier
main.pdf (1.15 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY NC ND - Paternité - Pas d'utilisation commerciale - Pas de modification

Dates et versions

hal-04551793 , version 1 (18-04-2024)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

  • HAL Id : hal-04551793 , version 1

Citer

Martin Pépin, Alfredo Viola. Asymptotic analysis and efficient random sampling of directed ordered acyclic graphs. 2023. ⟨hal-04551793⟩
0 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More