par Fiorini, Samuel 
;Joret, Gwenaël ;Schaudt, Oliver
Référence Mathematical programming, 182, 1-2, page (355–367)
Publication Publié, 2020-07-01
;Joret, Gwenaël ;Schaudt, OliverRéférence Mathematical programming, 182, 1-2, page (355–367)
Publication Publié, 2020-07-01
Article révisé par les pairs
| Résumé : | We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the literature and admits a straightforward 3-approximation algorithm since it is a special case of the vertex cover problem on a 3-uniform hypergraph. Recently, You, Wang, and Cao described an efficient 5/2-approximation algorithm for the unweighted version of the problem. Our main result is a 9/4-approximation algorithm for arbitrary weights, using the local ratio technique. We further conjecture that the problem admits a 2-approximation algorithm and give some support for the conjecture. This is in sharp contrast with the fact that the similar problem of deleting vertices to eliminate all triangles in a graph is known to be UGC-hard to approximate to within a ratio better than 3, as proved by Guruswami and Lee. |
