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- W4300485501 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." @default.
- W4300485501 created "2022-10-03" @default.
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- W4300485501 date "2018-02-20" @default.
- W4300485501 modified "2023-09-26" @default.
- W4300485501 title "Selection from heaps, row-sorted matrices and $X+Y$ using soft heaps" @default.
- W4300485501 doi "https://doi.org/10.48550/arxiv.1802.07041" @default.
- W4300485501 hasPublicationYear "2018" @default.
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