{"paper":{"title":"PTAS and Exact Algorithms for $r$-Gathering Problems on Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Soh Kumabe, Takanori Maehara","submitted_at":"2019-07-09T11:29:43Z","abstract_excerpt":"r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at least r users are assigned to every open facility. We aim to minimize the maximum distance between user and assigned facility. In general, this problem is NP-hard and admit an approximation algorithm with factor 3. It is known that the problem does not admit any approximation algorithm within a factor less than 3. In our another paper, we proved that this pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04087","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"}