{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WOQ66UKZMMK3H56AIGGKHD3ETI","short_pith_number":"pith:WOQ66UKZ","canonical_record":{"source":{"id":"1408.4944","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T10:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"b9da5213171c0f4c340ff0b8e5ed6a4afe6ef1e0384c83025f7f1d88e0eb0204","abstract_canon_sha256":"ebee3cc4407a6e4cab9c00d77936d9335c717cec3fe4530ae9d745ac0a893ad2"},"schema_version":"1.0"},"canonical_sha256":"b3a1ef51596315b3f7c0418ca38f649a03a370d6fdcca39ecba0c9673360def9","source":{"kind":"arxiv","id":"1408.4944","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4944","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4944v4","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4944","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"pith_short_12","alias_value":"WOQ66UKZMMK3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WOQ66UKZMMK3H56A","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WOQ66UKZ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WOQ66UKZMMK3H56AIGGKHD3ETI","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4944","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T10:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"b9da5213171c0f4c340ff0b8e5ed6a4afe6ef1e0384c83025f7f1d88e0eb0204","abstract_canon_sha256":"ebee3cc4407a6e4cab9c00d77936d9335c717cec3fe4530ae9d745ac0a893ad2"},"schema_version":"1.0"},"canonical_sha256":"b3a1ef51596315b3f7c0418ca38f649a03a370d6fdcca39ecba0c9673360def9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:00.255657Z","signature_b64":"Ev8zfTIvjx88ZqJC+uzCttJ986p/N/bAs0TtY/aEQct7H3hjBZggjmzQbH/h2aAz/XX1bR2wwGVsFDuonW08CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3a1ef51596315b3f7c0418ca38f649a03a370d6fdcca39ecba0c9673360def9","last_reissued_at":"2026-05-18T02:43:00.254993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:00.254993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4944","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17hXnBTVVyT7qbGXjqWj8kGssYYw3fpH7Nwz4ZO9xJat6Q1poRLxqHtGobdDOXy37CNwsigK+fLNjyCxoI7FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:05:30.821741Z"},"content_sha256":"a68c9efb8aa2324440e00242a669a50f39c683d61bc5c1a196540715eea479eb","schema_version":"1.0","event_id":"sha256:a68c9efb8aa2324440e00242a669a50f39c683d61bc5c1a196540715eea479eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WOQ66UKZMMK3H56AIGGKHD3ETI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation algorithms for Capacitated Facility Location Problem with Penalties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Neelima Gupta, Shubham Gupta","submitted_at":"2014-08-21T10:42:50Z","abstract_excerpt":"In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \\cite{charikar2001algorithms}, Jain et. al. \\cite{jain2003greedy} and Xu- Xu \\cite{xu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4944","kind":"arxiv","version":4},"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":"2026-05-18T02:43:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyq8s3f2kETDJtNG6WpCJ7eRaVQCrM1jHcsCma4c2je9FfE/AVluK9Yv3kWJJdDhu1ya6emVS0Q2sGvh97HSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:05:30.822277Z"},"content_sha256":"caf543d136fd4a76d07335b9bf0d78c59b4aaacae0a5de0117407fa56c81775a","schema_version":"1.0","event_id":"sha256:caf543d136fd4a76d07335b9bf0d78c59b4aaacae0a5de0117407fa56c81775a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/bundle.json","state_url":"https://pith.science/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/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":"2026-05-31T04:05:30Z","links":{"resolver":"https://pith.science/pith/WOQ66UKZMMK3H56AIGGKHD3ETI","bundle":"https://pith.science/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/bundle.json","state":"https://pith.science/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WOQ66UKZMMK3H56AIGGKHD3ETI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WOQ66UKZMMK3H56AIGGKHD3ETI","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":"ebee3cc4407a6e4cab9c00d77936d9335c717cec3fe4530ae9d745ac0a893ad2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T10:42:50Z","title_canon_sha256":"b9da5213171c0f4c340ff0b8e5ed6a4afe6ef1e0384c83025f7f1d88e0eb0204"},"schema_version":"1.0","source":{"id":"1408.4944","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4944","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4944v4","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4944","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"pith_short_12","alias_value":"WOQ66UKZMMK3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WOQ66UKZMMK3H56A","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WOQ66UKZ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:caf543d136fd4a76d07335b9bf0d78c59b4aaacae0a5de0117407fa56c81775a","target":"graph","created_at":"2026-05-18T02:43:00Z","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 address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \\cite{charikar2001algorithms}, Jain et. al. \\cite{jain2003greedy} and Xu- Xu \\cite{xu","authors_text":"Neelima Gupta, Shubham Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T10:42:50Z","title":"Approximation algorithms for Capacitated Facility Location Problem with Penalties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4944","kind":"arxiv","version":4},"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:a68c9efb8aa2324440e00242a669a50f39c683d61bc5c1a196540715eea479eb","target":"record","created_at":"2026-05-18T02:43:00Z","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":"ebee3cc4407a6e4cab9c00d77936d9335c717cec3fe4530ae9d745ac0a893ad2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T10:42:50Z","title_canon_sha256":"b9da5213171c0f4c340ff0b8e5ed6a4afe6ef1e0384c83025f7f1d88e0eb0204"},"schema_version":"1.0","source":{"id":"1408.4944","kind":"arxiv","version":4}},"canonical_sha256":"b3a1ef51596315b3f7c0418ca38f649a03a370d6fdcca39ecba0c9673360def9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3a1ef51596315b3f7c0418ca38f649a03a370d6fdcca39ecba0c9673360def9","first_computed_at":"2026-05-18T02:43:00.254993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:00.254993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ev8zfTIvjx88ZqJC+uzCttJ986p/N/bAs0TtY/aEQct7H3hjBZggjmzQbH/h2aAz/XX1bR2wwGVsFDuonW08CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:00.255657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4944","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a68c9efb8aa2324440e00242a669a50f39c683d61bc5c1a196540715eea479eb","sha256:caf543d136fd4a76d07335b9bf0d78c59b4aaacae0a5de0117407fa56c81775a"],"state_sha256":"6049406bb6aa21401eac2d72a2e8e6d783188ecc7c4a874a8ae7e0bc7d1bb37f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u7mIJK74s56w5aCvG15Zl1zUUVIEZdzELygVXiZB7YqJr3/mZgnOZc/576gA5DpySouLFbXhx4XXBH9RyTXvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:05:30.825100Z","bundle_sha256":"1876646fadfd483cb853566753a82c709693a61c9dcc34cc6ae25dd49ead814c"}}