TY - GEN

T1 - Parameterized orientable deletion

AU - Hanaka, Tesshu

AU - Katsikarelis, Ioannis

AU - Lampis, Michael

AU - Otachi, Yota

AU - Sikora, Florian

N1 - Funding Information:
Funding This work was financially supported by the “PHC Sakura” program (project GRAPA, number: 38593YJ), implemented by the French Ministry of Foreign Affairs, the French Ministry of Higher Education and Research and the Japan Society for Promotion of Science.
Publisher Copyright:
© Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Yota Otachi, and Florian Sikora.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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 log n-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, , the problem does not admit a (d + 2 − )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 know algorithm for this case.

AB - 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 log n-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, , the problem does not admit a (d + 2 − )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 know algorithm for this case.

UR - http://www.scopus.com/inward/record.url?scp=85049033592&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049033592&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SWAT.2018.24

DO - 10.4230/LIPIcs.SWAT.2018.24

M3 - Conference contribution

AN - SCOPUS:85049033592

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 241

EP - 2413

BT - 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018

A2 - Eppstein, David

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018

Y2 - 18 June 2018 through 20 June 2018

ER -