{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GPU6DN3XPHZEWLGSMWKSAX2JS5","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":"1fa0a6adf336a4461234c26766fda6f6d0e3d8bd4fdfc6a71fd456fb5187d3cf","cross_cats_sorted":["cs.DC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-02T09:55:43Z","title_canon_sha256":"6069359b91e34bf4554981db55c708548b9cdaaf1f41e43af0f8598efc655e5f"},"schema_version":"1.0","source":{"id":"1702.00787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00787","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00787v1","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00787","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"GPU6DN3XPHZE","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPU6DN3XPHZEWLGS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPU6DN3X","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:43658cb4f7d73154c6460148ed09ffbe08a08954bde4c3e724d4ba0d2365194a","target":"graph","created_at":"2026-05-18T00:51:29Z","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 consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algorithms obtain a solution with a bound of $\\frac{1}{n+1}$ times the optimum solution, with either $\\mathcal{O}\\left(m\\log n\\right)$ time and $\\mathcal{O}\\left(m n\\right)$ messages, or $\\mathcal{O}\\lef","authors_text":"Ananth Murthy, Chandan Yeshwanth, Shrisha Rao","cross_cats":["cs.DC","cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-02T09:55:43Z","title":"Distributed Approximation Algorithms for the Multiple Knapsack Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00787","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":"sha256:7e635a5ed3e3971bda61bdc8c7f145fdc581306aba23883c2fb64feb7a1fa03c","target":"record","created_at":"2026-05-18T00:51:29Z","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":"1fa0a6adf336a4461234c26766fda6f6d0e3d8bd4fdfc6a71fd456fb5187d3cf","cross_cats_sorted":["cs.DC","cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-02T09:55:43Z","title_canon_sha256":"6069359b91e34bf4554981db55c708548b9cdaaf1f41e43af0f8598efc655e5f"},"schema_version":"1.0","source":{"id":"1702.00787","kind":"arxiv","version":1}},"canonical_sha256":"33e9e1b77779f24b2cd26595205f4997604ee03651ea9e8f39c5be8b8d8d1133","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e9e1b77779f24b2cd26595205f4997604ee03651ea9e8f39c5be8b8d8d1133","first_computed_at":"2026-05-18T00:51:29.761796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:29.761796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X8aO/VQrKiqjL56oUxIUI0xFxhQSqpnPBxy6cqRmNdpkKaH1JAEz0FUSixHt7WDyNO01jM0J9+6IzDSqAVfjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:29.762277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e635a5ed3e3971bda61bdc8c7f145fdc581306aba23883c2fb64feb7a1fa03c","sha256:43658cb4f7d73154c6460148ed09ffbe08a08954bde4c3e724d4ba0d2365194a"],"state_sha256":"5b0289084811c1153efa97529e5a0b287a79ebda50ca845c2657b88127f2f0e1"}