License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.SOSA.2019.5
URN: urn:nbn:de:0030-drops-100315
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10031/
Kaplan, Haim ;
Kozma, László ;
Zamir, Or ;
Zwick, Uri
Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps
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 + sum_{i=1}^m log(k_i+1)) comparisons, where k_i is the number of items of the i-th list that belong to the overall set of k smallest items.
BibTeX - Entry
@InProceedings{kaplan_et_al:OASIcs:2018:10031,
author = {Haim Kaplan and L{\'a}szl{\'o} Kozma and Or Zamir and Uri Zwick},
title = {{Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps}},
booktitle = {2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
pages = {5:1--5:21},
series = {OpenAccess Series in Informatics (OASIcs)},
ISBN = {978-3-95977-099-6},
ISSN = {2190-6807},
year = {2018},
volume = {69},
editor = {Jeremy T. Fineman and Michael Mitzenmacher},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/10031},
URN = {urn:nbn:de:0030-drops-100315},
doi = {10.4230/OASIcs.SOSA.2019.5},
annote = {Keywords: selection, soft heap}
}
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Keywords: |
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selection, soft heap |
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Collection: |
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2nd Symposium on Simplicity in Algorithms (SOSA 2019) |
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Issue Date: |
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2018 |
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Date of publication: |
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08.01.2019 |
