{"paper":{"title":"Routing under Balance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Alina Ene, Gary Miller, Jakub Pachocki","submitted_at":"2016-03-30T01:09:47Z","abstract_excerpt":"We introduce the notion of balance for directed graphs: a weighted directed graph is $\\alpha$-balanced if for every cut $S \\subseteq V$, the total weight of edges going from $S$ to $V\\setminus S$ is within factor $\\alpha$ of the total weight of edges going from $V\\setminus S$ to $S$. Several important families of graphs are nearly balanced, in particular, Eulerian graphs (with $\\alpha = 1$) and residual graphs of $(1+\\epsilon)$-approximate undirected maximum flows (with $\\alpha=O(1/\\epsilon)$).\n  We use the notion of balance to give a more fine-grained understanding of several well-studied rou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09009","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"}