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dc.contributor.authorEstivill-Castro, Vladimir
dc.contributor.authorHeednacram, Apichat
dc.contributor.authorSuraweera, Francis
dc.contributor.editorHermann Maurer
dc.date.accessioned2017-05-03T14:16:01Z
dc.date.available2017-05-03T14:16:01Z
dc.date.issued2010
dc.date.modified2010-09-30T09:13:47Z
dc.identifier.issn0948695X
dc.identifier.doi10.3217/jucs-016-05-0622
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.
dc.description.peerreviewedYes
dc.description.publicationstatusYes
dc.format.extent461373 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglish
dc.language.isoeng
dc.publisherVerlag der Technischen Universität Graz
dc.publisher.placeAustria
dc.relation.ispartofstudentpublicationN
dc.relation.ispartofpagefrom622
dc.relation.ispartofpageto652
dc.relation.ispartofissue5
dc.relation.ispartofjournalJournal of Universal Computer Science
dc.relation.ispartofvolume15
dc.rights.retentionY
dc.subject.fieldofresearchAnalysis of Algorithms and Complexity
dc.subject.fieldofresearchMathematical Sciences
dc.subject.fieldofresearchInformation and Computing Sciences
dc.subject.fieldofresearchcode080201
dc.subject.fieldofresearchcode01
dc.subject.fieldofresearchcode08
dc.titleNP-completeness and FPT Results for Rectilinear Covering Problems
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyGriffith Sciences, School of Information and Communication Technology
gro.rights.copyright© 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.
gro.date.issued2010
gro.hasfulltextFull Text
gro.griffith.authorSuraweera, Francis
gro.griffith.authorHeednacram, Apichat
gro.griffith.authorEstivill-Castro, Vladimir


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