{"paper":{"title":"Distributed Strong Diameter Network Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Ofer Neiman","submitted_at":"2016-02-17T14:43:40Z","abstract_excerpt":"For a pair of positive parameters $D,\\chi$, a partition ${\\cal P}$ of the vertex set $V$ of an $n$-vertex graph $G = (V,E)$ into disjoint clusters of diameter at most $D$ each is called a $(D,\\chi)$ network decomposition, if the supergraph ${\\cal G}({\\cal P})$, obtained by contracting each of the clusters of ${\\cal P}$, can be properly $\\chi$-colored. The decomposition ${\\cal P}$ is said to be strong (resp., weak) if each of the clusters has strong (resp., weak) diameter at most $D$, i.e., if for every cluster $C \\in {\\cal P}$ and every two vertices $u,v \\in C$, the distance between them in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05437","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"}