Decision trees with minimum average depth for sorting eight elements

Handle URI:
http://hdl.handle.net/10754/583291
Title:
Decision trees with minimum average depth for sorting eight elements
Authors:
AbouEisha, Hassan M. ( 0000-0003-4560-7175 ) ; Chikalov, Igor; Moshkov, Mikhail ( 0000-0003-0085-9483 )
Abstract:
We 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Decision trees with minimum average depth for sorting eight elements 2015 Discrete Applied Mathematics
Publisher:
Elsevier BV
Journal:
Discrete Applied Mathematics
Issue Date:
19-Nov-2015
DOI:
10.1016/j.dam.2015.10.030
Type:
Article
ISSN:
0166218X
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0166218X1500517X
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAbouEisha, Hassan M.en
dc.contributor.authorChikalov, Igoren
dc.contributor.authorMoshkov, Mikhailen
dc.date.accessioned2015-12-07T10:01:20Zen
dc.date.available2015-12-07T10:01:20Zen
dc.date.issued2015-11-19en
dc.identifier.citationDecision trees with minimum average depth for sorting eight elements 2015 Discrete Applied Mathematicsen
dc.identifier.issn0166218Xen
dc.identifier.doi10.1016/j.dam.2015.10.030en
dc.identifier.urihttp://hdl.handle.net/10754/583291en
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.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0166218X1500517Xen
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.2015.10.030en
dc.subjectSortingen
dc.subjectDecision treeen
dc.subjectAverage depthen
dc.titleDecision trees with minimum average depth for sorting eight elementsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalDiscrete Applied Mathematicsen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorAbouEisha, Hassan M.en
kaust.authorChikalov, Igoren
kaust.authorMoshkov, Mikhailen
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