{"paper":{"title":"An FPT Algorithm for Diverse Minimum s-t Cuts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fedor V. Fomin, Krishnan Dehaleesan, Laure Morelle, P{\\aa}l Gr{\\o}n{\\aa}s Drange, Petr A. Golovach","submitted_at":"2026-07-03T12:35:53Z","abstract_excerpt":"We study the problem of finding a family of diverse minimum edge s-t cuts in a directed weighted graph G. Given integers k and d, the task is to decide whether G contains k minimum s-t cuts C_1, ..., C_k such that for any i,j in [k], the number of edges in the symmetric difference of C_i and C_j is at least d.\n  For d being 1 or 2, the problem corresponds to counting minimum s-t cuts in G, which is #P-complete [Provan and Ball, SICOMP 1983]. The problem is also known to be NP-complete already for k = 3 [de Berg, L\\'opez Mart\\'inez, Spieksma, ISAAC 2024]. Our main result shows that the problem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03266","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}