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We call this problem LSA-MinExcess, and show that it is equivalent to NZ-MinExcess: Given integral values per player, find a coalition with minimum excess whose player values do not sum up to $0$. Exploiting this representation, we prove that the nucleolus is computable in polynomial time for arboricity games, network strength games, and"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.29571","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-28T08:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"b7318ee789113cc4c9d6f986cdf3cba82a9682208ac8cfa9e156be104dc46384","abstract_canon_sha256":"d832964eaf215c2926d14beba0da61e18e8738bb0618b1589837a4c36a7419dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:48.061001Z","signature_b64":"OzRPKAUeu/a0p4Hd+s1yT9OW6lQPzk0x7CNTjtu8TQNvRFZE9akfKzTgQ5Pb6O1LP3k3XtTgOsaTQC35wUUmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b9477c01856253eafcfe3bd86ee75b1c016ca33ed8f981deb80a3e2a829b11","last_reissued_at":"2026-05-29T01:05:48.058938Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:48.058938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nucleolus Computation by Non-Zero-Constrained Optimization","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Antonia Ellerbrock, Daniel Ebert","submitted_at":"2026-05-28T08:17:50Z","abstract_excerpt":"We extend the list of games where the nucleolus is computable in polynomial time. 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