2016
DOI: 10.1016/j.jda.2015.11.001
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Near-optimal online multiselection in internal and external memory

Abstract: We introduce an online version of the multiselection problem, in which q selection queries are requested on an unsorted array of nelements. We provide the first online algorithm that is 1-competitive with the offline algorithm proposed by Kaligosi et al. [14] in terms of comparison complexity. Our algorithm also supports online searchqueries efficiently. We then extend our algorithm to the dynamic setting, while retaining online functionality, by supporting arbitrary insertions and deletions on the array. Assu… Show more

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Cited by 5 publications
(14 citation statements)
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“…Their data structure uses B + o(B) + O(n + q ′ log n) comparisons, where q ′ is the number of search, insert, and delete operations. The crucial difference between our solution and that of Barbay et al [BGRSS15,BGSS16] is how we handle insertions. Their analysis assumes every insertion is preceded by a search and therefore insertion must take Ω(log n) time.…”
Section: Online Dynamic Multiple Selectionmentioning
confidence: 94%
See 3 more Smart Citations
“…Their data structure uses B + o(B) + O(n + q ′ log n) comparisons, where q ′ is the number of search, insert, and delete operations. The crucial difference between our solution and that of Barbay et al [BGRSS15,BGSS16] is how we handle insertions. Their analysis assumes every insertion is preceded by a search and therefore insertion must take Ω(log n) time.…”
Section: Online Dynamic Multiple Selectionmentioning
confidence: 94%
“…We can further support additional insertions, deletions and queries. Data structures for online dynamic multiple selection were previously known [BGRSS15,BGSS16], but the way we handle dynamism is more efficient, allowing for all the use cases mentioned here. We discuss this in Section 2.…”
Section: Example Scenariosmentioning
confidence: 99%
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“…In some sense, this research approaches a unification of different ordered data structures into a single theory of a best data structure for ordered data. Optimal priority queues (a single gap ∆ 1 ), online dynamic multiple selection [BGSS16] (gaps are separated by queried ranks), and binary search trees (every element is in its own gap) are special cases of our solution. This paper closes the book theoretically in the gap-based model proposed in [SW20]; any further work in this research direction requires generalization of the gap model, stated in [SW20] as open problem 1.…”
Section: Introductionmentioning
confidence: 99%