Selection from heaps, row-sorted matrices, and X + Y using soft heaps

Haim Kaplan, László Kozma, Or Zamir, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We use soft heaps to obtain simpler optimal algorithms for selecting the k-th smallest item, and the set of k smallest items, from a heap-ordered tree, from a collection of sorted lists, and from X + Y , where X and Y are two unsorted sets. Our results match, and in some ways extend and improve, classical results of Frederickson (1993) and Frederickson and Johnson (1982). In particular, for selecting the k-th smallest item, or the set of k smallest items, from a collection of m sorted lists we obtain a new optimal “output-sensitive” algorithm that performs only O(m + Ʃmi=1 log(ki + 1)) comparisons, where ki is the number of items of the i-th list that belong to the overall set of k smallest items.

Original languageEnglish
Title of host publication2nd Symposium on Simplicity in Algorithms, SOSA 2019 - Co-located with the 30th ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
EditorsJeremy T. Fineman, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770996
DOIs
StatePublished - Jan 2019
Event2nd Symposium on Simplicity in Algorithms, SOSA 2019 - San Diego, United States
Duration: 8 Jan 20199 Jan 2019

Publication series

NameOpenAccess Series in Informatics
Volume69
ISSN (Print)2190-6807

Conference

Conference2nd Symposium on Simplicity in Algorithms, SOSA 2019
Country/TerritoryUnited States
CitySan Diego
Period8/01/199/01/19

Keywords

  • Selection
  • soft heap

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