Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 96 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 24 tok/s
GPT-5 High 36 tok/s Pro
GPT-4o 102 tok/s
GPT OSS 120B 434 tok/s Pro
Kimi K2 198 tok/s Pro
2000 character limit reached

B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load (2303.04722v1)

Published 8 Mar 2023 in cs.DS and cs.CG

Abstract: Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of $n$ keys from a totally ordered universe in this context. We introduce a two-layer data structure called $(\alpha,\varepsilon)$-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory. Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the {\em expected} search, update, and storage, efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have $O(\varepsilon{-1} + \log_\alpha n)$ block-reads, that $(\alpha, \varepsilon)$-RBSTs have an asymptotic load-factor of at least $(1-\varepsilon)$ for every $\varepsilon \in (0,1/2]$, and that dynamic updates perform $O(\varepsilon{-1} + \log_\alpha(n)/\alpha)$ block-writes, i.e. $O(1/\varepsilon)$ writes if $\alpha=\Omega(\frac{\log n}{\log \log n} )$. Thus $(\alpha, \varepsilon)$-RBSTs provide improved search, storage-, and write-efficiency bounds in regard to the known, uniquely represented B-Treap [Golovin; ICALP'09].

Citations (1)
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

Summary

We haven't generated a summary for this paper yet.

Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube