SimdQuickHeap: The QuickHeap Reconsidered

[2604.25681] SimdQuickHeap: The QuickHeap Reconsidered Skip to main content Search Submit Donate Log in Computer Science > Data Structures and Algorithms arXiv:2604.25681 (cs) [Submitted on 28 Apr 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: SimdQuickHeap: The QuickHeap Reconsidered Authors: Johannes Breitling , Ragnar Groot Koerkamp , Marvin Williams View PDF HTML (experimental) Abstract: Priority queues are data structures that maintain a dynamic collection of elements and allow inserting new elements and removing the smallest element. The most widely known and used priority queue is likely the implicit binary heap, even though it has frequent cache misses and is hard to optimize using e.g. SIMD instructions. We introduce the SimdQuickHeap, a variant of the QuickHeap that was introduced by Navarro and Paredes in 2010. As suggested by the name, the data structure bears some similarity to QuickSort. We modify the data layout of the original QuickHeap to have all pivots adjacent in memory, with elements between consecutive pivots stored in dedicated buckets. This allows efficient SIMD implementations for both partitioning of buckets and scanning the list of pivots to find the bucket to append newly inserted elements to. The SimdQuickHeap has amortized expected complexity $O(\log n)$ per operation, which improves to $O(\frac 1W\log n)$ in non-degenerate cases, where $W$ is the number of words in a SIMD register. In this case, the I/O-complexity is amortized $O(\frac 1B)$ per push and $O(\frac 1B \log_2 \frac nM)$ per pop. In synthetic benchmarks, the SimdQuickHeap is $1.2\times$ to $1.7\times$ as fast as the monotone radix heap, the next-best competitor, and $1.4\times$ to $2.8\times$ as fast as the superscalar sample queue, the fastest comparison-based priority queue. The SimdQuickHeap needs around $1.5\log_2 n$ comparisons and $\log_2 n$ nanoseconds per pair of push and pop operations. On graph benchmarks with Dijkstra's shortest path algorithm and Jarník-Prim's minimum spanning tree algorithm, the SimdQuickHeap is consistently the fastest. Comments: Update to match published ESA 2026 version; 19 pages; 6 figures Subjects: Data Structures and Algorithms (cs.DS) ACM classes: F.2.2 Cite as: arXiv:2604.25681 [cs.DS] (or arXiv:2604.25681v3 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2604.25681 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.4230/LIPIcs.ESA.2026.16 Focus to learn more DOI(s) linking to related resources Submission history From: Ragnar Groot Koerkamp [ view email ] [v1] Tue, 28 Apr 2026 14:12:17 UTC (447 KB) [v2] Thu, 9 Jul 2026 08:10:54 UTC (441 KB) [v3] Thu, 27 Aug 2026 11:00:33 UTC (483 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.DS < prev | next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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