TY - GEN
T1 - Selection from heaps, row-sorted matrices, and X + Y using soft heaps
AU - Kaplan, Haim
AU - Kozma, László
AU - Zamir, Or
AU - Zwick, Uri
N1 - Publisher Copyright:
© Haim Kaplan, László Kozma, Or Zamir, and Uri Zwick.
PY - 2019/1
Y1 - 2019/1
N2 - 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.
AB - 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.
KW - Selection
KW - soft heap
UR - http://www.scopus.com/inward/record.url?scp=85069221178&partnerID=8YFLogxK
U2 - 10.4230/OASIcs.SOSA.2019.5
DO - 10.4230/OASIcs.SOSA.2019.5
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AN - SCOPUS:85069221178
T3 - OpenAccess Series in Informatics
BT - 2nd Symposium on Simplicity in Algorithms, SOSA 2019 - Co-located with the 30th ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
A2 - Fineman, Jeremy T.
A2 - Mitzenmacher, Michael
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 2nd Symposium on Simplicity in Algorithms, SOSA 2019
Y2 - 8 January 2019 through 9 January 2019
ER -