{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:QLKSTBIELYQOI2SWIIWWTFLQKH","short_pith_number":"pith:QLKSTBIE","schema_version":"1.0","canonical_sha256":"82d52985045e20e46a56422d69957051eb19f82a03ecd7dce15199cc9256c35a","source":{"kind":"arxiv","id":"2104.09312","version":1},"attestation_state":"computed","paper":{"title":"Minimizing the total weighted pairwise connection time in network construction problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Igor Averbakh","submitted_at":"2021-04-19T13:51:08Z","abstract_excerpt":"It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a fixed overall construction speed. The problem is strongly NP-hard even on stars. We present polynomial algorithms for the problem on trees with a fixed number of leaves, and on general networks with a fixed number of relevant pairs."},"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":"2104.09312","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2021-04-19T13:51:08Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"35046a7bce70881a04640e95cea786c33288584df9cedefb15c2e6589140ce42","abstract_canon_sha256":"d4d6f6de9238641be1cbed3da382661817ee57c82b94ac16df3e891a61875531"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:33:11.865979Z","signature_b64":"afhuipKd/3JhB7FTpABcaNR9Eee3X4MpX+tkU3+U8ZrBK+WJX4esyRVJFZ4DCoZrGe0fom40A23ZxigUlnukDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d52985045e20e46a56422d69957051eb19f82a03ecd7dce15199cc9256c35a","last_reissued_at":"2026-07-05T02:33:11.865572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:33:11.865572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimizing the total weighted pairwise connection time in network construction problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Igor Averbakh","submitted_at":"2021-04-19T13:51:08Z","abstract_excerpt":"It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a fixed overall construction speed. The problem is strongly NP-hard even on stars. We present polynomial algorithms for the problem on trees with a fixed number of leaves, and on general networks with a fixed number of relevant pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.09312","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.09312/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2104.09312","created_at":"2026-07-05T02:33:11.865636+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.09312v1","created_at":"2026-07-05T02:33:11.865636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.09312","created_at":"2026-07-05T02:33:11.865636+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLKSTBIELYQO","created_at":"2026-07-05T02:33:11.865636+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLKSTBIELYQOI2SW","created_at":"2026-07-05T02:33:11.865636+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLKSTBIE","created_at":"2026-07-05T02:33:11.865636+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/QLKSTBIELYQOI2SWIIWWTFLQKH","json":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH.json","graph_json":"https://pith.science/api/pith-number/QLKSTBIELYQOI2SWIIWWTFLQKH/graph.json","events_json":"https://pith.science/api/pith-number/QLKSTBIELYQOI2SWIIWWTFLQKH/events.json","paper":"https://pith.science/paper/QLKSTBIE"},"agent_actions":{"view_html":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH","download_json":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH.json","view_paper":"https://pith.science/paper/QLKSTBIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.09312&json=true","fetch_graph":"https://pith.science/api/pith-number/QLKSTBIELYQOI2SWIIWWTFLQKH/graph.json","fetch_events":"https://pith.science/api/pith-number/QLKSTBIELYQOI2SWIIWWTFLQKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH/action/storage_attestation","attest_author":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH/action/author_attestation","sign_citation":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH/action/citation_signature","submit_replication":"https://pith.science/pith/QLKSTBIELYQOI2SWIIWWTFLQKH/action/replication_record"}},"created_at":"2026-07-05T02:33:11.865636+00:00","updated_at":"2026-07-05T02:33:11.865636+00:00"}