{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B7IXT3INULNLVD5646XWTCTCDH","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":"4e85ede5c36f7a42403bc84eda293aa2aea57bdbec1be38462fdfbd6fc8be793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-10T16:16:21Z","title_canon_sha256":"60c71ebfc2eea3294d0133de4393119ee1bcc445c8e1ef529d65325a4b7c6533"},"schema_version":"1.0","source":{"id":"1509.03212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03212","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03212v1","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03212","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"B7IXT3INULNL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B7IXT3INULNLVD56","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B7IXT3IN","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:b4e2582c9054fb40dd5e7c6bd767f1b13465432b4d60c5f17c2eefd84a03a6b6","target":"graph","created_at":"2026-05-18T01:33:25Z","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":"We present the first non-trivial online algorithms for the non-uniform, multicommodity buy-at-bulk (MC-BB) network design problem in undirected and directed graphs. Our competitive ratios qualitatively match the best known approximation factors for the corresponding offline problems. The main engine for our results is an online reduction theorem of MC-BB problems to their single-sink (SS-BB) counterparts. We use the concept of junction-tree solutions (Chekuri et al., FOCS 2006) that play an important role in solving the offline versions of the problem via a greedy subroutine -- an inherently o","authors_text":"Alina Ene, Debmalya Panigrahi, Deeparnab Chakrabarty, Ravishankar Krishnaswamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-10T16:16:21Z","title":"Online Buy-at-Bulk Network Design"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03212","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":"sha256:464a1bf66027938381fea1a19ac45bb9694a4a1beef3668f9a82449445d25f7b","target":"record","created_at":"2026-05-18T01:33:25Z","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":"4e85ede5c36f7a42403bc84eda293aa2aea57bdbec1be38462fdfbd6fc8be793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-10T16:16:21Z","title_canon_sha256":"60c71ebfc2eea3294d0133de4393119ee1bcc445c8e1ef529d65325a4b7c6533"},"schema_version":"1.0","source":{"id":"1509.03212","kind":"arxiv","version":1}},"canonical_sha256":"0fd179ed0da2daba8fbee7af698a6219dc7463d9f3e7ce505c46d7bca26a32d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fd179ed0da2daba8fbee7af698a6219dc7463d9f3e7ce505c46d7bca26a32d6","first_computed_at":"2026-05-18T01:33:25.045847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:25.045847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8z4FFMie+p11Fc0JLqyo2l+8SOOg1QJBLY50acrNIAlJry6d0g7HcXCzkzhwqyatm7QvB592EGMAUfz/z/hXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:25.046377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:464a1bf66027938381fea1a19ac45bb9694a4a1beef3668f9a82449445d25f7b","sha256:b4e2582c9054fb40dd5e7c6bd767f1b13465432b4d60c5f17c2eefd84a03a6b6"],"state_sha256":"971a28ab088add6eadce88aca36db4fad37a5cc789c873ca0526b321b89167ab"}