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dc.contributor.authorEstivill-Castro, Vladimiren_US
dc.contributor.authorHeednacram, Apichaten_US
dc.contributor.authorSuraweera, Francisen_US
dc.date.accessioned2017-05-03T14:15:59Z
dc.date.available2017-05-03T14:15:59Z
dc.date.issued2009en_US
dc.identifier.issn10846654en_US
dc.identifier.doi10.1145/1498698.1626535en_US
dc.identifier.urihttp://hdl.handle.net/10072/29702
dc.description.abstractWe present efficient algorithms to solve the LINE COVER problem exactly. In this NP-complete problem, the inputs are n points in the plane and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines. Our approach is based on fixed-parameter tractability, and in particular, kernelization. We propose several reduction rules to transform instances of LINE COVER into equivalent smaller instances. Once instances are no longer susceptible to these reduction rules, we obtain a problem kernel whose size is bounded by a polynomial function of the parameter k and does not depend on the size n of the input. Our algorithms provide exact solutions and are easy to implement. We also describe the design of algorithms to solve the corresponding optimization problem exactly. We experimentally evaluated ten variants of the algorithms to determine the impact and trade-offs of several reduction rules. We show that our approach provides tractability for a larger range of values of the parameter and larger inputs, improving the execution time by several orders of magnitude with respect to previously known algorithms.en_US
dc.description.peerreviewedYesen_US
dc.description.publicationstatusYesen_US
dc.format.extent477661 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglishen_US
dc.language.isoen_US
dc.publisherAssociation for Computing Machineryen_US
dc.publisher.placeUSAen_US
dc.relation.ispartofstudentpublicationNen_US
dc.relation.ispartofpagefrom1en_US
dc.relation.ispartofpageto26en_US
dc.relation.ispartofjournalJournal of Experimental Algorithmicsen_US
dc.relation.ispartofvolume14en_US
dc.rights.retentionYen_US
dc.subject.fieldofresearchAnalysis of Algorithms and Complexityen_US
dc.subject.fieldofresearchcode080201en_US
dc.titleReduction Rules Deliver Efficient FPT Algorithms for Covering Points with Linesen_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 ACM, 2009. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Journal of Experimental Algorithmics (JEA), Volume 14, December 2009, http://doi.acm.org/10.1145/1498698.1626535en_US
gro.date.issued2015-06-12T05:02:41Z
gro.hasfulltextFull Text


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