{"paper":{"title":"Complexity and Algorithms for Unary Translocation Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Adrian Micl\\u{a}u\\c{s}, Alexandru Popa, Andrei Popa, Maria Constantin","submitted_at":"2026-06-07T02:26:12Z","abstract_excerpt":"Given a finite set of integers $A$, a \\emph{unary translocation} produces a new set $A' = A \\cup \\{u,v\\}$, where $u$ and $v$ are nonnegative integers satisfying $x+y=u+v$ for some $x,y\\in A$. For an input set $A$ and a target set $B$, the \\emph{unary translocation distance} is the minimum number of unary translocations required to obtain a superset containing $B$. In this paper, we study this problem from both theoretical and computational perspectives. We prove that computing the unary translocation distance is strongly NP-hard, thereby answering an open question raised by \\citet{ConstantinMi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08412","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/2606.08412/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"}