{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:X4XNH7BLH4PWM4RMX3YMI4DIN2","short_pith_number":"pith:X4XNH7BL","schema_version":"1.0","canonical_sha256":"bf2ed3fc2b3f1f66722cbef0c470686ebc2af3f3cd510e2cbeb9c79c7bd81561","source":{"kind":"arxiv","id":"1303.0160","version":1},"attestation_state":"computed","paper":{"title":"Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.OC","authors_text":"Abraham P. Punnen, Daniel Karapetyan, Piyashat Sripratak","submitted_at":"2013-03-01T12:53:38Z","abstract_excerpt":"We consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem (BBQP) with m+n variables. A closed form formula is developed to compute the average objective function value A of all solutions in O(mn) time. However, computing the median objective function value of the solutions is shown to be NP-hard. Also, we show that any solution with objective function value no worse than A dominates at least 2^{m+n-2} solutions and this bound is the best possible. Further, we show that such a solution can be identified in O(mn) time and hence the domina"},"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":"1303.0160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-01T12:53:38Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"eb0b2f61799f5bec5133f2f94c42adaa57fb7b56e0eb6047638c77eba6a9b466","abstract_canon_sha256":"09514f2a450da27303d0234c9cc3b50f3b6da986f32de7a60ef61cd4aef01ee1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:32.698858Z","signature_b64":"oxcW7BMB6zjjdOfqEw9GirsNM/GdJn+LWT2Ta7o9Q9K3fZqwgGw58AOyNujIL+2OFR2N/oHGOyCu3YTqaugVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf2ed3fc2b3f1f66722cbef0c470686ebc2af3f3cd510e2cbeb9c79c7bd81561","last_reissued_at":"2026-05-18T02:30:32.698456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:32.698456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.OC","authors_text":"Abraham P. Punnen, Daniel Karapetyan, Piyashat Sripratak","submitted_at":"2013-03-01T12:53:38Z","abstract_excerpt":"We consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem (BBQP) with m+n variables. A closed form formula is developed to compute the average objective function value A of all solutions in O(mn) time. However, computing the median objective function value of the solutions is shown to be NP-hard. Also, we show that any solution with objective function value no worse than A dominates at least 2^{m+n-2} solutions and this bound is the best possible. Further, we show that such a solution can be identified in O(mn) time and hence the domina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0160","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":"1303.0160","created_at":"2026-05-18T02:30:32.698520+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.0160v1","created_at":"2026-05-18T02:30:32.698520+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0160","created_at":"2026-05-18T02:30:32.698520+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4XNH7BLH4PW","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4XNH7BLH4PWM4RM","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4XNH7BL","created_at":"2026-05-18T12:28:06.772260+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/X4XNH7BLH4PWM4RMX3YMI4DIN2","json":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2.json","graph_json":"https://pith.science/api/pith-number/X4XNH7BLH4PWM4RMX3YMI4DIN2/graph.json","events_json":"https://pith.science/api/pith-number/X4XNH7BLH4PWM4RMX3YMI4DIN2/events.json","paper":"https://pith.science/paper/X4XNH7BL"},"agent_actions":{"view_html":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2","download_json":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2.json","view_paper":"https://pith.science/paper/X4XNH7BL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.0160&json=true","fetch_graph":"https://pith.science/api/pith-number/X4XNH7BLH4PWM4RMX3YMI4DIN2/graph.json","fetch_events":"https://pith.science/api/pith-number/X4XNH7BLH4PWM4RMX3YMI4DIN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2/action/storage_attestation","attest_author":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2/action/author_attestation","sign_citation":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2/action/citation_signature","submit_replication":"https://pith.science/pith/X4XNH7BLH4PWM4RMX3YMI4DIN2/action/replication_record"}},"created_at":"2026-05-18T02:30:32.698520+00:00","updated_at":"2026-05-18T02:30:32.698520+00:00"}