{"paper":{"title":"Fixed-Parameter Algorithms for DAG Partitioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI"],"primary_cat":"cs.DS","authors_text":"Andr\\'e Nichterlein, Falk H\\\"uffner, Morgan Chopin, Ond\\v{r}ej Such\\'y, Ren\\'e van Bevern, Robert Bredereck, Sepp Hartung","submitted_at":"2016-11-27T09:04:03Z","abstract_excerpt":"Finding the origin of short phrases propagating through the web has been formalized by Leskovec et al. [ACM SIGKDD 2009] as DAG Partitioning: given an arc-weighted directed acyclic graph on $n$ vertices and $m$ arcs, delete arcs with total weight at most $k$ such that each resulting weakly-connected component contains exactly one sink---a vertex without outgoing arcs. DAG Partitioning is NP-hard.\n  We show an algorithm to solve DAG Partitioning in $O(2^k \\cdot (n+m))$ time, that is, in linear time for fixed $k$. We complement it with linear-time executable data reduction rules. Our experiments"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08809","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"}