eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-01-08
5:1
5:21
10.4230/OASIcs.SOSA.2019.5
article
Selection from Heaps, Row-Sorted Matrices, and X+Y Using Soft Heaps
Kaplan, Haim
Kozma, László
Zamir, Or
Zwick, Uri
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.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol069-sosa2019/OASIcs.SOSA.2019.5/OASIcs.SOSA.2019.5.pdf
selection
soft heap