{"paper":{"title":"Almost Universally Optimal Distributed Laplacian Solvers via Low-Congestion Shortcuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Bernhard Haeupler, Christoph Lenzen, Goran Zuzic, Ioannis Anagnostides, Themis Gouleakis","submitted_at":"2021-09-11T01:45:34Z","abstract_excerpt":"In this paper, we refine the (almost) \\emph{existentially optimal} distributed Laplacian solver recently developed by Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS `21) into an (almost) \\emph{universally optimal} distributed Laplacian solver.\n  Specifically, when the topology is known, we show that any Laplacian system on an $n$-node graph with \\emph{shortcut quality} $\\text{SQ}(G)$ can be solved within $n^{o(1)} \\text{SQ}(G) \\log(1/\\varepsilon)$ rounds, where $\\varepsilon$ is the required accuracy. This almost matches our lower bound which guarantees that any correct algorithm on $G$ require"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.05151","kind":"arxiv","version":3},"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/2109.05151/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"}