Polynomial Delay Algorithm for Minimal Chordal Completions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2022

Polynomial Delay Algorithm for Minimal Chordal Completions

Abstract

Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In [8] (Pods 2017) Carmeli et al. proved that all minimal chordal completions or equivalently all proper tree decompositions of a graph can be listed in incremental polynomial time using exponential space. The total running time of their algorithm is quadratic in the number of solutions and the existence of an algorithm whose complexity depends only linearly on the number of solutions remained open. We close this question by providing a polynomial delay algorithm to solve this problem which, moreover, uses polynomial space. Our algorithm relies on Proximity Search, a framework recently introduced by Conte and Uno [12] (Stoc 2019) which has been shown powerful to obtain polynomial delay algorithms, but generally requires exponential space. In order to obtain a polynomial space algorithm for our problem, we introduce a new general method called canonical path reconstruction to design polynomial delay and polynomial space algorithms based on proximity search.
Fichier principal
Vignette du fichier
LIPIcs-ICALP-2022-33.pdf (765.65 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive

Dates and versions

hal-03829955 , version 1 (26-10-2022)

Identifiers

Cite

Caroline Brosse, Vincent Limouzy, Arnaud Mary. Polynomial Delay Algorithm for Minimal Chordal Completions. 49th International Colloquium on Automata, Languages, and Programming (ICALP), 2022, Paris, France. ⟨10.4230/LIPIcs.ICALP.2022.33⟩. ⟨hal-03829955⟩
51 View
42 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More