Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7-Free and P_8-Free Chordal Graphs

Abstract : In [M. M. Kanté, V. Limouzy, A. Mary, and L. Nourine. On the enumeration of minimal dominating sets and related notions. SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014.] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-free chordal graphs. In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k. In particular, we give O(n+m) and O(n^3 * m) delays algorithms in the classes of P_7-free and P_8-free chordal graphs. As for P_k-free chordal graphs for k >= 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01786826
Contributor : Oscar Defrain <>
Submitted on : Friday, November 29, 2019 - 9:18:04 AM
Last modification on : Sunday, December 1, 2019 - 1:27:09 AM

File

12345.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01786826, version 2

Collections

Citation

Oscar Defrain, Lhouari Nourine. Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7-Free and P_8-Free Chordal Graphs. 2019. ⟨hal-01786826v2⟩

Share

Metrics

Record views

8

Files downloads

6