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The best previous algorithm that routed $\\Omega("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.2554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T14:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"64aee1258adbbd1d73b7b8f8e5da193701161b08508f74b45df0ef5b957d5082","abstract_canon_sha256":"b9f92ccab96b99bcfab776e4038890ee2990bde39c56cd0e54500cc4491dc099"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:22.843521Z","signature_b64":"lyY7Ec7Oa0qr0MNVnPjbyjtTM22ugha95Ig5XpEnK5Ioo9OeaPHGKCtqHukuK24ILw59ke6ut++1CBsSOM8gAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f94c2f20f11729a7fbced3daab6c2a5b98bf053d53fd2bb3641cfe5c88c2161","last_reissued_at":"2026-05-18T04:18:22.842945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:22.842945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Routing in Undirected Graphs with Constant Congestion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Julia Chuzhoy","submitted_at":"2011-07-13T14:04:11Z","abstract_excerpt":"Given an undirected graph G=(V,E), a collection (s_1,t_1),...,(s_k,t_k) of k source-sink pairs, and an integer c, the goal in the Edge Disjoint Paths with Congestion problem is to connect maximum possible number of the source-sink pairs by paths, so that the maximum load on any edge (called edge congestion) does not exceed c.\n  We show an efficient randomized algorithm to route $\\Omega(OPT/\\poly\\log k)$ source-sink pairs with congestion at most 14, where OPT is the maximum number of pairs that can be simultaneously routed on edge-disjoint paths. 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