{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T6KMF4QPCFZJU7545U62VNWCUW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b9f92ccab96b99bcfab776e4038890ee2990bde39c56cd0e54500cc4491dc099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T14:04:11Z","title_canon_sha256":"64aee1258adbbd1d73b7b8f8e5da193701161b08508f74b45df0ef5b957d5082"},"schema_version":"1.0","source":{"id":"1107.2554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2554","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2554v1","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2554","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"T6KMF4QPCFZJ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T6KMF4QPCFZJU754","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T6KMF4QP","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:8d38f255990e0357e1ad5f48a4c20e792a6538d240299588e6ebb7e88f681b2e","target":"graph","created_at":"2026-05-18T04:18:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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. The best previous algorithm that routed $\\Omega(","authors_text":"Julia Chuzhoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T14:04:11Z","title":"Routing in Undirected Graphs with Constant Congestion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2554","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ac873d0b92f2b2cf069f515de0e4a6a0f2a4ed5e1570bde706dd6e16bbf7acbe","target":"record","created_at":"2026-05-18T04:18:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b9f92ccab96b99bcfab776e4038890ee2990bde39c56cd0e54500cc4491dc099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-13T14:04:11Z","title_canon_sha256":"64aee1258adbbd1d73b7b8f8e5da193701161b08508f74b45df0ef5b957d5082"},"schema_version":"1.0","source":{"id":"1107.2554","kind":"arxiv","version":1}},"canonical_sha256":"9f94c2f20f11729a7fbced3daab6c2a5b98bf053d53fd2bb3641cfe5c88c2161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f94c2f20f11729a7fbced3daab6c2a5b98bf053d53fd2bb3641cfe5c88c2161","first_computed_at":"2026-05-18T04:18:22.842945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:22.842945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lyY7Ec7Oa0qr0MNVnPjbyjtTM22ugha95Ig5XpEnK5Ioo9OeaPHGKCtqHukuK24ILw59ke6ut++1CBsSOM8gAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:22.843521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac873d0b92f2b2cf069f515de0e4a6a0f2a4ed5e1570bde706dd6e16bbf7acbe","sha256:8d38f255990e0357e1ad5f48a4c20e792a6538d240299588e6ebb7e88f681b2e"],"state_sha256":"67df1e99690a4ccefb8443de942ed1ea2fef751d37efbfaecd80d2e27e66dec6"}