{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MXPNXP7DOKZHQGPLCOIUHR35HE","short_pith_number":"pith:MXPNXP7D","canonical_record":{"source":{"id":"1704.06928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T14:41:26Z","cross_cats_sorted":["math.NA","math.OC"],"title_canon_sha256":"6a5c353564ce7a6b250fa60ee7259024798f0b9bf63cf26a7d3c0de1e3d7d370","abstract_canon_sha256":"cdf079ce88d9384a88f98d7379351d50e921c3369b8aa2b393a863b1acdc49d7"},"schema_version":"1.0"},"canonical_sha256":"65dedbbfe372b27819eb139143c77d39350494747aca81374c9b120f45399a3d","source":{"kind":"arxiv","id":"1704.06928","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06928","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06928v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06928","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"MXPNXP7DOKZH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MXPNXP7DOKZHQGPL","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MXPNXP7D","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MXPNXP7DOKZHQGPLCOIUHR35HE","target":"record","payload":{"canonical_record":{"source":{"id":"1704.06928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T14:41:26Z","cross_cats_sorted":["math.NA","math.OC"],"title_canon_sha256":"6a5c353564ce7a6b250fa60ee7259024798f0b9bf63cf26a7d3c0de1e3d7d370","abstract_canon_sha256":"cdf079ce88d9384a88f98d7379351d50e921c3369b8aa2b393a863b1acdc49d7"},"schema_version":"1.0"},"canonical_sha256":"65dedbbfe372b27819eb139143c77d39350494747aca81374c9b120f45399a3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:55.315028Z","signature_b64":"KaskMKCGGLjPXWC9BdTG3hWfzxCqBpHIzw/yHD70O6cnAkV/oWEkC+TzeI+BdQBGc6vnHhP4+56W6U40ehkNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65dedbbfe372b27819eb139143c77d39350494747aca81374c9b120f45399a3d","last_reissued_at":"2026-05-18T00:45:55.314361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:55.314361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.06928","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gUIhVYkbv3MSC6Me/0/NBA5+HyFfiovOnmsa2GnA5PCilJD14AV5Jf2iEVypyhNOzziF/TC9GxCmhq5aUPiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:06:32.816207Z"},"content_sha256":"7d17cd80f9d1e71387ce931f4e2647da2ce6590929b348fcbbfd8e8bff64c26e","schema_version":"1.0","event_id":"sha256:7d17cd80f9d1e71387ce931f4e2647da2ce6590929b348fcbbfd8e8bff64c26e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MXPNXP7DOKZHQGPLCOIUHR35HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Rui Diao, Ya-Feng Liu, Yu-Hong Dai","submitted_at":"2017-04-23T14:41:26Z","abstract_excerpt":"The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals $\\left\\{[a_{i,1},a_{i,2}]\\right\\}_{i=1}^n$ and a target integer $T,$ the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target $T$ but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high prob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06928","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":"2026-05-18T00:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itDAqhdIEymlPqBdUdx02Gocg4poT6wYFLDvOMwEZyYxVo7CtDWacohFxkgCE2a60JotAU6hJgPU/zrGoyDsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:06:32.816592Z"},"content_sha256":"6e51626a737eb93016491e733ca78f2c308a4a68da360f8b5c676ac02c267c51","schema_version":"1.0","event_id":"sha256:6e51626a737eb93016491e733ca78f2c308a4a68da360f8b5c676ac02c267c51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/bundle.json","state_url":"https://pith.science/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/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":"2026-06-07T02:06:32Z","links":{"resolver":"https://pith.science/pith/MXPNXP7DOKZHQGPLCOIUHR35HE","bundle":"https://pith.science/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/bundle.json","state":"https://pith.science/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXPNXP7DOKZHQGPLCOIUHR35HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MXPNXP7DOKZHQGPLCOIUHR35HE","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":"cdf079ce88d9384a88f98d7379351d50e921c3369b8aa2b393a863b1acdc49d7","cross_cats_sorted":["math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T14:41:26Z","title_canon_sha256":"6a5c353564ce7a6b250fa60ee7259024798f0b9bf63cf26a7d3c0de1e3d7d370"},"schema_version":"1.0","source":{"id":"1704.06928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.06928","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1704.06928v1","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.06928","created_at":"2026-05-18T00:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"MXPNXP7DOKZH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MXPNXP7DOKZHQGPL","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MXPNXP7D","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:6e51626a737eb93016491e733ca78f2c308a4a68da360f8b5c676ac02c267c51","target":"graph","created_at":"2026-05-18T00:45:55Z","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":"The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals $\\left\\{[a_{i,1},a_{i,2}]\\right\\}_{i=1}^n$ and a target integer $T,$ the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target $T$ but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high prob","authors_text":"Rui Diao, Ya-Feng Liu, Yu-Hong Dai","cross_cats":["math.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T14:41:26Z","title":"A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06928","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":"sha256:7d17cd80f9d1e71387ce931f4e2647da2ce6590929b348fcbbfd8e8bff64c26e","target":"record","created_at":"2026-05-18T00:45:55Z","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":"cdf079ce88d9384a88f98d7379351d50e921c3369b8aa2b393a863b1acdc49d7","cross_cats_sorted":["math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-23T14:41:26Z","title_canon_sha256":"6a5c353564ce7a6b250fa60ee7259024798f0b9bf63cf26a7d3c0de1e3d7d370"},"schema_version":"1.0","source":{"id":"1704.06928","kind":"arxiv","version":1}},"canonical_sha256":"65dedbbfe372b27819eb139143c77d39350494747aca81374c9b120f45399a3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65dedbbfe372b27819eb139143c77d39350494747aca81374c9b120f45399a3d","first_computed_at":"2026-05-18T00:45:55.314361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:55.314361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KaskMKCGGLjPXWC9BdTG3hWfzxCqBpHIzw/yHD70O6cnAkV/oWEkC+TzeI+BdQBGc6vnHhP4+56W6U40ehkNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:55.315028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.06928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d17cd80f9d1e71387ce931f4e2647da2ce6590929b348fcbbfd8e8bff64c26e","sha256:6e51626a737eb93016491e733ca78f2c308a4a68da360f8b5c676ac02c267c51"],"state_sha256":"15248541801a750043ec54caa978ce2ed8ffcf70587a1edce190ac353ef80e78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAwA94/QHbUBR/4o+pfHxUzMA+2Wo7eFlU3gvEOuAHqwqXgw6aKYOUCIAe3XivjUHMexERDXfbL3JjPlM+l6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:06:32.818522Z","bundle_sha256":"9af41aa7663930289163d69722e61a449ab3f7a75d456627969fc3ae0a92c217"}}