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dc.contributor.authorEstivill-Castro, Vladimiren_US
dc.contributor.authorHeednacram, Apichaten_US
dc.contributor.authorSuraweera, Francisen_US
dc.contributor.editorHermann Maureren_US
dc.date.accessioned2017-04-24T11:31:13Z
dc.date.available2017-04-24T11:31:13Z
dc.date.issued2010en_US
dc.date.modified2010-09-30T09:13:47Z
dc.identifier.issn0948695Xen_US
dc.identifier.doi10.3217/jucs-016-05-0622en_AU
dc.identifier.urihttp://hdl.handle.net/10072/34022
dc.description.abstractThis paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the RECTILINEAR LINE COVER where the inputs are n points in Rd and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficient fixed-parameter tractable (FPT) algorithms. The second problem is the RECTILINEAR k-LINKS SPANNING PATH PROBLEM where the inputs are also n points in Rd and a positive integer k but here we are asked to answer if there is a piecewise linear path through these n points having at most k line-segments (links) where these line-segments are axisparallel. We prove that this second problem is FPT under the assumption that no two line-segments share the same line. The third problem is the RECTILINEAR HYPERPLANE COVER problem and we are asked to cover a set of n points in d dimensions with k axis-parallel hyperplanes of d - 1 dimensions. We also demonstrate this has an FPT-algorithm. Previous to the results above, only conjectures were enunciated over several years on the NP-completeness of the RECTILINEAR MINIMUM LINK TRAVELING SALESMAN PROBLEM, the MINIMUM LINK SPANNING PATH PROBLEM and the RECTILINEAR HYPERPLANE COVER. We provide the proof that the RECTILINEAR MINIMUM LINK TRAVELING SALESMAN PROBLEM and the RECTILINEAR MINIMUM LINK SPANNING PATH PROBLEM are NP-complete by a reduction from the ONE-IN-THREE 3-SAT problem. The NP-completeness of the RECTILINEAR HYPERPLANE COVER problem is proved by a reduction from 3-SAT. This suggests dealing with the intractability just discovered with fixed-parameter tractability. Moreover, if we extend our problems to a finite set of orientations, our approach proves these problems remain FPT.en_US
dc.description.peerreviewedYesen_US
dc.description.publicationstatusYesen_AU
dc.format.extent461373 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglishen_US
dc.language.isoen_AU
dc.publisherVerlag der Technischen Universität Grazen_US
dc.publisher.placeAustriaen_US
dc.relation.ispartofstudentpublicationNen_AU
dc.relation.ispartofpagefrom622en_US
dc.relation.ispartofpageto652en_US
dc.relation.ispartofissue5en_US
dc.relation.ispartofjournalJournal of Universal Computer Scienceen_US
dc.relation.ispartofvolume15en_US
dc.rights.retentionYen_AU
dc.subject.fieldofresearchAnalysis of Algorithms and Complexityen_US
dc.subject.fieldofresearchcode080201en_US
dc.titleNP-completeness and FPT Results for Rectilinear Covering Problemsen_US
dc.typeJournal articleen_US
dc.type.descriptionC1 - Peer Reviewed (HERDC)en_US
dc.type.codeC - Journal Articlesen_US
gro.facultyGriffith Sciences, School of Information and Communication Technologyen_US
gro.rights.copyrightCopyright 2010 J.UCS. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.en_AU
gro.date.issued2010
gro.hasfulltextFull Text


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