Distance-preserving orderings in graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2016

Distance-preserving orderings in graphs

Abstract

For every connected graph G, a subgraph H of G is isometric if the distance between any two vertices in H is the same in H as in G. A distance-preserving elimination ordering of G is a total ordering of its vertex-set V (G), denoted (v1; v2;...,vn), such that any subgraph Gi = G n (v1; v2;..., vi) with 1 ≤ i < n is isometric. This kind of ordering has been introduced by Chepoi in his study on weakly modular graphs [11]. We prove that it is NP-complete to decide whether such ordering exists for a given graph | even if it has diameter at most 2. Then, we prove on the positive side that the problem of computing a distance-preserving ordering when there exists one is fixed-parameter-tractable in the treewidth. Lastly, we describe a heuristic in order to compute a distance-preserving ordering when there exists one that we compare to an exact exponential time algorithm and to an ILP formulation for the problem.
Nous étudions les ordres d’élimination des sommets préservant les distances dans les graphes.
Fichier principal
Vignette du fichier
dpo_RR2019 (1).pdf (1.15 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01393523 , version 1 (07-11-2016)
hal-01393523 , version 2 (28-03-2019)

Identifiers

  • HAL Id : hal-01393523 , version 2

Cite

David Coudert, Guillaume Ducoffe, Nicolas Nisse, Mauricio Soto. Distance-preserving orderings in graphs. [Research Report] RR-8973, Inria Sophia Antipolis. 2016, pp.1-23. ⟨hal-01393523v2⟩
370 View
357 Download

Share

Gmail Facebook X LinkedIn More