Parameterized orientable deletion

Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Yota Otachi, Florian Sikora

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publication16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
EditorsDavid Eppstein
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages241-2413
Number of pages2173
ISBN (Electronic)9783959770682
DOIs
Publication statusPublished - Jun 1 2018
Externally publishedYes
Event16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 - Malmo, Sweden
Duration: Jun 18 2018Jun 20 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume101
ISSN (Print)1868-8969

Conference

Conference16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
Country/TerritorySweden
CityMalmo
Period6/18/186/20/18

All Science Journal Classification (ASJC) codes

  • Software

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