{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GFXRGDTT73X5GEQEBQB46RCFVY","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":"97c20b28a6fa05ee0183a2066c1a815d8261350d92600bd1a4b88252b8335cce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-07T09:14:59Z","title_canon_sha256":"858c65e4afb7a3e0d7d032aa99cd8a8dbe01a1017c25db5ebe9e111d319e6d42"},"schema_version":"1.0","source":{"id":"1905.02424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02424","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02424v2","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02424","created_at":"2026-05-17T23:41:36Z"},{"alias_kind":"pith_short_12","alias_value":"GFXRGDTT73X5","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GFXRGDTT73X5GEQE","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GFXRGDTT","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:1aee5e7a49b98efdc8f1052faa52888565afd3b5d02defba5ebaf0b830e8f690","target":"graph","created_at":"2026-05-17T23:41:36Z","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 the Equal-Subset-Sum problem, we are given a set $S$ of $n$ integers and the problem is to decide if there exist two disjoint nonempty subsets $A,B \\subseteq S$, whose elements sum up to the same value. The problem is NP-complete. The state-of-the-art algorithm runs in $O^{*}(3^{n/2}) \\le O^{*}(1.7321^n)$ time and is based on the meet-in-the-middle technique. In this paper, we improve upon this algorithm and give $O^{*}(1.7088^n)$ worst case Monte Carlo algorithm. This answers the open problem from Woeginger's inspirational survey.\n  Additionally, we analyse the polynomial space algorithm f","authors_text":"Jakub Pawlewicz, Jesper Nederlof, Karol W\\k{e}grzycki, Marcin Mucha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-07T09:14:59Z","title":"Equal-Subset-Sum Faster Than the Meet-in-the-Middle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02424","kind":"arxiv","version":2},"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":"sha256:494705d4101d457048bd096b82a9538654bafb1f733e0f5920a1307c8a84dbd6","target":"record","created_at":"2026-05-17T23:41:36Z","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":"97c20b28a6fa05ee0183a2066c1a815d8261350d92600bd1a4b88252b8335cce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-05-07T09:14:59Z","title_canon_sha256":"858c65e4afb7a3e0d7d032aa99cd8a8dbe01a1017c25db5ebe9e111d319e6d42"},"schema_version":"1.0","source":{"id":"1905.02424","kind":"arxiv","version":2}},"canonical_sha256":"316f130e73feefd312040c03cf4445ae2e5e573454e9a66db9e92d4bc775edb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"316f130e73feefd312040c03cf4445ae2e5e573454e9a66db9e92d4bc775edb6","first_computed_at":"2026-05-17T23:41:36.309385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:36.309385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GyNqOGwew6UrJkM9aaoWzbWXXZhmMuO8gbGWDg+DcdOF13mIIsLsqsVrS0eHZteQ9vYaiU0GnQW+WM0oRQZuDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:36.309949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:494705d4101d457048bd096b82a9538654bafb1f733e0f5920a1307c8a84dbd6","sha256:1aee5e7a49b98efdc8f1052faa52888565afd3b5d02defba5ebaf0b830e8f690"],"state_sha256":"478f4f86a27e3f017fa5c68f1b189a1223b1cdd7844a372fdeb4127394f7a69e"}