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dc.contributor.authorEstivill-Castro, Vladimir
dc.contributor.authorHeednacram, Apichat
dc.contributor.authorSuraweera, Francis
dc.date.accessioned2017-05-03T14:15:59Z
dc.date.available2017-05-03T14:15:59Z
dc.date.issued2009
dc.identifier.issn10846654
dc.identifier.doi10.1145/1498698.1626535
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.
dc.description.peerreviewedYes
dc.description.publicationstatusYes
dc.format.extent477661 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglish
dc.language.isoeng
dc.publisherAssociation for Computing Machinery
dc.publisher.placeUSA
dc.relation.ispartofstudentpublicationN
dc.relation.ispartofpagefrom1
dc.relation.ispartofpageto26
dc.relation.ispartofjournalJournal of Experimental Algorithmics
dc.relation.ispartofvolume14
dc.rights.retentionY
dc.subject.fieldofresearchAnalysis of Algorithms and Complexity
dc.subject.fieldofresearchPure Mathematics
dc.subject.fieldofresearchApplied Mathematics
dc.subject.fieldofresearchComputation Theory and Mathematics
dc.subject.fieldofresearchcode080201
dc.subject.fieldofresearchcode0101
dc.subject.fieldofresearchcode0102
dc.subject.fieldofresearchcode0802
dc.titleReduction Rules Deliver Efficient FPT Algorithms for Covering Points with Lines
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyGriffith Sciences, School of Information and Communication Technology
gro.rights.copyright© 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/10.1145/1498698.1626535
gro.date.issued2015-06-12T05:02:41Z
gro.hasfulltextFull Text
gro.griffith.authorSuraweera, Francis
gro.griffith.authorHeednacram, Apichat
gro.griffith.authorEstivill-Castro, Vladimir


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