{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BWXUSHIN2CD4ZZDVEKUXMLUF3O","short_pith_number":"pith:BWXUSHIN","schema_version":"1.0","canonical_sha256":"0daf491d0dd087cce47522a9762e85db83918042d7f672114bbc60adebe1ca8c","source":{"kind":"arxiv","id":"1104.2882","version":1},"attestation_state":"computed","paper":{"title":"Minimum Weight Cycles and Triangles: Equivalences and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Liam Roditty, Virginia Vassilevska Williams","submitted_at":"2011-04-14T19:32:10Z","abstract_excerpt":"We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a directed n-node graph with edge weights in {-M,..., M} and no negative cycles can be efficiently reduced to finding a minimum weight triangle in an Theta(n)-node undirected graph with weights in {1,...,O(M)}. Roughly speaking, our reductions imply the following surprising phenomenon: a minimum cycle with an arbitrary number of weighted edges can be \"encoded\" usi"},"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":"1104.2882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-04-14T19:32:10Z","cross_cats_sorted":[],"title_canon_sha256":"3e5e7f21bd9670167111a0288b241b1e945da7d73627d0203dee34c86f4f0888","abstract_canon_sha256":"be524e2bf1a5c43db64d1655da99621ca128ea2e7359c1425928d416e93ad54f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:26.669577Z","signature_b64":"rDxT3eBl7fNuhgBBRGOtZIuqw0afuOXSmHS7Dn6r2a8aN1z7XokMc+nB4BhheEIYVg7T5QFIAS/6i41matBSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0daf491d0dd087cce47522a9762e85db83918042d7f672114bbc60adebe1ca8c","last_reissued_at":"2026-05-18T04:24:26.668971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:26.668971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum Weight Cycles and Triangles: Equivalences and Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Liam Roditty, Virginia Vassilevska Williams","submitted_at":"2011-04-14T19:32:10Z","abstract_excerpt":"We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a directed n-node graph with edge weights in {-M,..., M} and no negative cycles can be efficiently reduced to finding a minimum weight triangle in an Theta(n)-node undirected graph with weights in {1,...,O(M)}. Roughly speaking, our reductions imply the following surprising phenomenon: a minimum cycle with an arbitrary number of weighted edges can be \"encoded\" usi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2882","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.2882","created_at":"2026-05-18T04:24:26.669093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.2882v1","created_at":"2026-05-18T04:24:26.669093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2882","created_at":"2026-05-18T04:24:26.669093+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWXUSHIN2CD4","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWXUSHIN2CD4ZZDV","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWXUSHIN","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O","json":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O.json","graph_json":"https://pith.science/api/pith-number/BWXUSHIN2CD4ZZDVEKUXMLUF3O/graph.json","events_json":"https://pith.science/api/pith-number/BWXUSHIN2CD4ZZDVEKUXMLUF3O/events.json","paper":"https://pith.science/paper/BWXUSHIN"},"agent_actions":{"view_html":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O","download_json":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O.json","view_paper":"https://pith.science/paper/BWXUSHIN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.2882&json=true","fetch_graph":"https://pith.science/api/pith-number/BWXUSHIN2CD4ZZDVEKUXMLUF3O/graph.json","fetch_events":"https://pith.science/api/pith-number/BWXUSHIN2CD4ZZDVEKUXMLUF3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O/action/storage_attestation","attest_author":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O/action/author_attestation","sign_citation":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O/action/citation_signature","submit_replication":"https://pith.science/pith/BWXUSHIN2CD4ZZDVEKUXMLUF3O/action/replication_record"}},"created_at":"2026-05-18T04:24:26.669093+00:00","updated_at":"2026-05-18T04:24:26.669093+00:00"}