{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QERA63OX3US4V7INIHJJ3KI2TI","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":"b707ecfd6ae4ac37ff34de4dde278fac580c452c28e33073a0515b2baac50ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-26T03:03:57Z","title_canon_sha256":"bea7aea4de00315fa0d603d34b04057141711df01ae3a68e7500ad2515313e04"},"schema_version":"1.0","source":{"id":"1610.08154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08154","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08154v1","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08154","created_at":"2026-05-18T01:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"QERA63OX3US4","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QERA63OX3US4V7IN","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QERA63OX","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:6cebbeb3aabee2effb1674dcf70da85a2ab4b20fe66d7a213d7352b95ebfbd4d","target":"graph","created_at":"2026-05-18T01:01:14Z","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 fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at most g jobs are active at any given time. The duration for which a machine is active (i.e., \"on\") is referred to as its active time. The goal is to find a feasible schedule for all jobs, minimizing the total active time. When preemption is allowed at integer time points, we show that a minimal feasible schedule already yields a 3-approximation (and this boun","authors_text":"Jessica Chang, Koyel Mukherjee, Samir Khuller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-26T03:03:57Z","title":"LP Rounding and Combinatorial Algorithms for Minimizing Active and Busy Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08154","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:d2730bb00a5d92fb030213216882c68cd2033660648efbe4460351e8257c161d","target":"record","created_at":"2026-05-18T01:01:14Z","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":"b707ecfd6ae4ac37ff34de4dde278fac580c452c28e33073a0515b2baac50ff9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-26T03:03:57Z","title_canon_sha256":"bea7aea4de00315fa0d603d34b04057141711df01ae3a68e7500ad2515313e04"},"schema_version":"1.0","source":{"id":"1610.08154","kind":"arxiv","version":1}},"canonical_sha256":"81220f6dd7dd25cafd0d41d29da91a9a232749a1c3282ec84ff30b9187c931a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81220f6dd7dd25cafd0d41d29da91a9a232749a1c3282ec84ff30b9187c931a4","first_computed_at":"2026-05-18T01:01:14.900675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:14.900675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"krFeFGGV2jada0mIuUY3sz4uxWVBkFY8sE9yasSJQ6QRb978K0t7z4gP53V2UnGMCk/WI+/IePmmfm7TVh8AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:14.901185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2730bb00a5d92fb030213216882c68cd2033660648efbe4460351e8257c161d","sha256:6cebbeb3aabee2effb1674dcf70da85a2ab4b20fe66d7a213d7352b95ebfbd4d"],"state_sha256":"29123e2cceacfaa6d9a0a1e5fc4c4eed634e73f47aea0d9f3a3f0aeeca572275"}