{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BOP5VHJDV4B4NCIEYXLWDHN66Q","short_pith_number":"pith:BOP5VHJD","canonical_record":{"source":{"id":"1805.07809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-20T18:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"b9c74fb19aef4f5dba17ab80a6dae59a3ec8aabce00cfc72583ca0ee070c9d88","abstract_canon_sha256":"ad06db36a88f9d819951842ad775182791f84307603397992b76fd4d8c72c5dd"},"schema_version":"1.0"},"canonical_sha256":"0b9fda9d23af03c68904c5d7619dbef4054e07267fdd022fedcfad1393c20836","source":{"kind":"arxiv","id":"1805.07809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07809","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07809v1","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07809","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"BOP5VHJDV4B4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOP5VHJDV4B4NCIE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOP5VHJD","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BOP5VHJDV4B4NCIEYXLWDHN66Q","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-20T18:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"b9c74fb19aef4f5dba17ab80a6dae59a3ec8aabce00cfc72583ca0ee070c9d88","abstract_canon_sha256":"ad06db36a88f9d819951842ad775182791f84307603397992b76fd4d8c72c5dd"},"schema_version":"1.0"},"canonical_sha256":"0b9fda9d23af03c68904c5d7619dbef4054e07267fdd022fedcfad1393c20836","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:32.476373Z","signature_b64":"e+FagReBVJML+5l/FolgJlk6SljY/EyU5/b7++3RBR78wcF5sxdxuNizmMcu2vIlrHASB6x035GGAGBhXqIDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b9fda9d23af03c68904c5d7619dbef4054e07267fdd022fedcfad1393c20836","last_reissued_at":"2026-05-18T00:15:32.475866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:32.475866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07809","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26WcV5xMhz90MiCQjXDvb+eHzM7fzMSqd0tdLl+JsttXdN+8I3wcauvL4VCq+spJzRALGMOeB37aZJOL84lNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:31:43.491731Z"},"content_sha256":"26b5c5abdc7c94295996ff40b9863ace51bda1d0bd9fd100354fa8387112ad77","schema_version":"1.0","event_id":"sha256:26b5c5abdc7c94295996ff40b9863ace51bda1d0bd9fd100354fa8387112ad77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BOP5VHJDV4B4NCIEYXLWDHN66Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Strategies for Robust Combinatorial Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hanna Sumita, Yasushi Kawase","submitted_at":"2018-05-20T18:03:40Z","abstract_excerpt":"In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our goal is to find a randomized strategy (i.e., a probability distribution over the independent sets) that maximizes the expected objective value. To solve the problem, we propose two types of schemes for designing approximation algorithms. One scheme is for the case when objective functions are linear. It first finds an approximately optimal aggregated strategy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07809","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZPei3KRBI6LBstN5cCVmOTpg/lVwrj8IZw2BkA+JuJtVH4GIB73Q4jYu56KHy9pfvp0o1G8VaKt/DeTvt26AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:31:43.492074Z"},"content_sha256":"86701b88f5c2d115810663ecca0540785e509d0ef81bfa45ca3af3c47c96c3bf","schema_version":"1.0","event_id":"sha256:86701b88f5c2d115810663ecca0540785e509d0ef81bfa45ca3af3c47c96c3bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/bundle.json","state_url":"https://pith.science/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T17:31:43Z","links":{"resolver":"https://pith.science/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q","bundle":"https://pith.science/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/bundle.json","state":"https://pith.science/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BOP5VHJDV4B4NCIEYXLWDHN66Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BOP5VHJDV4B4NCIEYXLWDHN66Q","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":"ad06db36a88f9d819951842ad775182791f84307603397992b76fd4d8c72c5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-20T18:03:40Z","title_canon_sha256":"b9c74fb19aef4f5dba17ab80a6dae59a3ec8aabce00cfc72583ca0ee070c9d88"},"schema_version":"1.0","source":{"id":"1805.07809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07809","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07809v1","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07809","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"BOP5VHJDV4B4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOP5VHJDV4B4NCIE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOP5VHJD","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:86701b88f5c2d115810663ecca0540785e509d0ef81bfa45ca3af3c47c96c3bf","target":"graph","created_at":"2026-05-18T00:15:32Z","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":"In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our goal is to find a randomized strategy (i.e., a probability distribution over the independent sets) that maximizes the expected objective value. To solve the problem, we propose two types of schemes for designing approximation algorithms. One scheme is for the case when objective functions are linear. It first finds an approximately optimal aggregated strategy","authors_text":"Hanna Sumita, Yasushi Kawase","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-20T18:03:40Z","title":"Randomized Strategies for Robust Combinatorial Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07809","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":"sha256:26b5c5abdc7c94295996ff40b9863ace51bda1d0bd9fd100354fa8387112ad77","target":"record","created_at":"2026-05-18T00:15:32Z","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":"ad06db36a88f9d819951842ad775182791f84307603397992b76fd4d8c72c5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-20T18:03:40Z","title_canon_sha256":"b9c74fb19aef4f5dba17ab80a6dae59a3ec8aabce00cfc72583ca0ee070c9d88"},"schema_version":"1.0","source":{"id":"1805.07809","kind":"arxiv","version":1}},"canonical_sha256":"0b9fda9d23af03c68904c5d7619dbef4054e07267fdd022fedcfad1393c20836","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b9fda9d23af03c68904c5d7619dbef4054e07267fdd022fedcfad1393c20836","first_computed_at":"2026-05-18T00:15:32.475866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:32.475866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e+FagReBVJML+5l/FolgJlk6SljY/EyU5/b7++3RBR78wcF5sxdxuNizmMcu2vIlrHASB6x035GGAGBhXqIDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:32.476373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26b5c5abdc7c94295996ff40b9863ace51bda1d0bd9fd100354fa8387112ad77","sha256:86701b88f5c2d115810663ecca0540785e509d0ef81bfa45ca3af3c47c96c3bf"],"state_sha256":"d72342d075773efefcbb952694bea2dc61df56f1fc332bac546cef049bd2b0c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5MKN7O9ALs2JU2HWaYLwn5IXSu/AP4v0w1HoA9rhk1luYnRwGHdMAVkBQONiQERgDA9hzGYAxL8nuiC6KS4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T17:31:43.493959Z","bundle_sha256":"6e422926fb5caaf81beebb27aea37066eaf28eac11496fa57ad061252ff424ea"}}