{"paper":{"title":"A Randomised Approach to Distributed Sorting","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DC","cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Sam Olesker-Taylor","submitted_at":"2025-02-07T16:57:48Z","abstract_excerpt":"We introduce and analyse a new, extremely simple, randomised sorting algorithm:\n  - choose a pair of indices $\\{i, j\\}$ according to some distribution $q$;\n  - sort the elements in positions $i$ and $j$ of the array in ascending order.\n  Choosing $q_{\\{i,j\\}} \\propto 1/|j - i|$ yields an order-$n (\\log n)^2$ sorting time. We call it the harmonic sorter.\n  The sorter trivially parallelises in the asynchronous setting, yielding a linear speed-up. We also exhibit a low-communication, synchronous version with a linear speed-up.\n  We compare and contrast this algorithm with other sorters, and discu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05082","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.05082/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}