{"paper":{"title":"Fully Dynamic Maximal Independent Set with Sublinear Update Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Baruch Schieber, Krzysztof Onak, Sepehr Assadi, Shay Solomon","submitted_at":"2018-02-27T03:56:48Z","abstract_excerpt":"A maximal independent set (MIS) can be maintained in an evolving $m$-edge graph by simply recomputing it from scratch in $O(m)$ time after each update. But can it be maintained in time sublinear in $m$ in fully dynamic graphs?\n  We answer this fundamental open question in the affirmative. We present a deterministic algorithm with amortized update time $O(\\min\\{\\Delta,m^{3/4}\\})$, where $\\Delta$ is a fixed bound on the maximum degree in the graph and $m$ is the (dynamically changing) number of edges.\n  We further present a distributed implementation of our algorithm with $O(\\min\\{\\Delta,m^{3/4}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09709","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":""},"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"}