UWSpace staff members will be away from May 5th to 9th, 2025. We will not be responding to emails during this time. If there are any urgent issues, please contact GSPA at gsrecord@uwaterloo.ca. If any login or authentication issues arise during this time, please wait until UWSpace Staff members return on May 12th for support.
 

Selectable Heaps and Their Application to Lazy Search Trees

dc.contributor.advisorMunro, Ian
dc.contributor.authorZhang, Lingyi
dc.date.accessioned2021-04-29T13:52:24Z
dc.date.available2021-04-29T13:52:24Z
dc.date.issued2021-04-29
dc.date.submitted2021-04-21
dc.description.abstractWe show the O(log n) time extract minimum function of efficient priority queues can be generalized to the extraction of the k smallest elements in O(k log(n/k)) time. We first show the heap-ordered tree selection of Kaplan et al. can be applied on the heap-ordered trees of the classic Fibonacci heap to support the extraction in O(k \log(n/k)) amortized time. We then show selection is possible in a priority queue with optimal worst-case guarantees by applying heap-ordered tree selection on Brodal queues, supporting the operation in O(k log(n/k)) worst-case time. Via a reduction from the multiple selection problem, Ω(k log(n/k)) time is necessary. We then apply the result to the lazy search trees of Sandlund & Wild, creating a new interval data structure based on selectable heaps. This gives optimal O(B+n) lazy search tree performance, lowering insertion complexity into a gap Δi to O(log(n/|Δi|))$ time. An O(1)-time merge operation is also made possible under certain conditions. If Brodal queues are used, all runtimes of the lazy search tree can be made worst-case. The presented data structure uses soft heaps of Chazelle, biased search trees, and efficient priority queues in a non-trivial way, approaching the theoretically-best data structure for ordered data.en
dc.identifier.urihttp://hdl.handle.net/10012/16921
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectpriority queuesen
dc.subjectFibonacci heapen
dc.subjectdata structureen
dc.subjectalgorithmen
dc.titleSelectable Heaps and Their Application to Lazy Search Treesen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorMunro, Ian
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Zhang_Lingyi.pdf
Size:
294.84 KB
Format:
Adobe Portable Document Format
Description:

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
6.4 KB
Format:
Item-specific license agreed upon to submission
Description: