{"paper":{"title":"Reducing a Target Interval to a Few Exact Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Erik Jan van Leeuwen, Jesper Nederlof, Ruben van der Zwaan","submitted_at":"2012-08-21T09:28:50Z","abstract_excerpt":"Many combinatorial problems involving weights can be formulated as a so-called ranged problem. That is, their input consists of a universe $U$, a (succinctly-represented) set family $\\mathcal{F} \\subseteq 2^{U}$, a weight function $\\omega:U \\rightarrow \\{1,...,N\\}$, and integers $0 \\leq l \\leq u \\leq \\infty$. Then the problem is to decide whether there is an $X \\in \\mathcal{F}$ such that $l \\leq \\sum_{e \\in X}\\omega(e) \\leq u$. Well-known examples of such problems include Knapsack, Subset Sum, Maximum Matching, and Traveling Salesman. In this paper, we develop a generic method to transform a r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4225","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":""},"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"}