Parameterized Orientable Deletion

Tesshu Hanaka (1) , Ioannis Katsikarelis (2) , Michael Lampis (2) , Yota Otachi (3) , Florian Sikora (2)

1 autre
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 Kumamoto Gakuen University

A graph is d-orientable if its edges can be oriented so that the maximum in-degree of the resulting digraph is at most d. d-orientability is a well-studied concept with close connections to fundamental graph-theoretic notions and applications as a load balancing problem. In this paper we consider the d-ORIENTABLE DELETION problem: given a graph G=(V,E), delete the minimum number of vertices to make G d-orientable. We contribute a number of results that improve the state of the art on this problem. Specifically: - We show that the problem is W[2]-hard and logn-inapproximable with respect to k, the number of deleted vertices. This closes the gap in the problem's approximability.- We completely characterize the parameterized complexity of the problem on chordal graphs: it is FPT parameterized by d+k, but W-hard for each of the parameters d,k separately. - We show that, under the SETH, for all d,ϵ, the problem does not admit a (d+2−ϵ)tw, algorithm where tw is the graph's treewidth, resolving as a special case an open problem on the complexity of PSEUDOFOREST DELETION. - We show that the problem is W-hard parameterized by the input graph's clique-width. Complementing this, we provide an algorithm running in time dO(d⋅cw), showing that the problem is FPT by d+cw, and improving the previously best known algorithm for this case.

Mots clés: Graph orientations; FPT algorithms; Treewidth; SETH

Domaines: Informatique [cs]

Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Yota Otachi, Florian Sikora. Parameterized Orientable Deletion. SWAT 2018, Jun 2018, Malmö, Sweden. pp.24:1-24:13. ⟨hal-02075097⟩