{"paper":{"title":"Optimal Bounds for Private Minimum Spanning Trees via Input Perturbation","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.CR","cs.LG"],"primary_cat":"cs.DS","authors_text":"Hanwen Zhang, Hao Wu, Lukas Retschmeier, Rasmus Pagh","submitted_at":"2024-12-13T13:22:39Z","abstract_excerpt":"We study the problem of privately releasing an approximate minimum spanning tree (MST). Given a graph $G = (V, E, \\vec{W})$ where $V$ is a set of $n$ vertices, $E$ is a set of $m$ undirected edges, and $ \\vec{W} \\in \\mathbb{R}^{|E|} $ is an edge-weight vector, our goal is to publish an approximate MST under edge-weight differential privacy, as introduced by Sealfon in PODS 2016, where $V$ and $E$ are considered public and the weight vector is private. Our neighboring relation is $\\ell_\\infty$-distance on weights: for a sensitivity parameter $\\Delta_\\infty$, graphs $ G = (V, E, \\vec{W}) $ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10130","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/2412.10130/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"}