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dc.contributor.authorAbouEisha, Hassan M.
dc.contributor.authorChikalov, Igor
dc.contributor.authorMoshkov, Mikhail
dc.date.accessioned2015-12-07T10:01:20Z
dc.date.available2015-12-07T10:01:20Z
dc.date.issued2015-11-19
dc.identifier.citationDecision trees with minimum average depth for sorting eight elements 2015 Discrete Applied Mathematics
dc.identifier.issn0166218X
dc.identifier.doi10.1016/j.dam.2015.10.030
dc.identifier.urihttp://hdl.handle.net/10754/583291
dc.description.abstractWe prove that the minimum average depth of a decision tree for sorting 8 pairwise different elements is equal to 620160/8!. We show also that each decision tree for sorting 8 elements, which has minimum average depth (the number of such trees is approximately equal to 8.548×10^326365), has also minimum depth. Both problems were considered by Knuth (1998). To obtain these results, we use tools based on extensions of dynamic programming which allow us to make sequential optimization of decision trees relative to depth and average depth, and to count the number of decision trees with minimum average depth.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0166218X1500517X
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 19 November 2015. DOI: 10.1016/j.dam.2015.10.030
dc.subjectSorting
dc.subjectDecision tree
dc.subjectAverage depth
dc.titleDecision trees with minimum average depth for sorting eight elements
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalDiscrete Applied Mathematics
dc.eprint.versionPost-print
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personAbouEisha, Hassan M.
kaust.personChikalov, Igor
kaust.personMoshkov, Mikhail
refterms.dateFOA2017-11-19T00:00:00Z


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