{"paper":{"title":"Parallel Metric Tree Embedding based on an Algebraic View on Moore-Bellman-Ford","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Christoph Lenzen, Stephan Friedrichs","submitted_at":"2015-09-30T07:51:48Z","abstract_excerpt":"A \\emph{metric tree embedding} of expected \\emph{stretch~$\\alpha \\geq 1$} maps a weighted $n$-node graph $G = (V, E, \\omega)$ to a weighted tree $T = (V_T, E_T, \\omega_T)$ with $V \\subseteq V_T$ such that, for all $v,w \\in V$, $\\operatorname{dist}(v, w, G) \\leq \\operatorname{dist}(v, w, T)$ and $operatorname{E}[\\operatorname{dist}(v, w, T)] \\leq \\alpha \\operatorname{dist}(v, w, G)$. Such embeddings are highly useful for designing fast approximation algorithms, as many hard problems are easy to solve on tree instances. However, to date the best parallel $(\\operatorname{polylog} n)$-depth algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09047","kind":"arxiv","version":4},"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"}