{"paper":{"title":"Data-compression for Parametrized Counting Problems on Sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Dimitrios M. Thilikos, Eun Jung Kim, Maria Serna","submitted_at":"2018-09-21T14:52:04Z","abstract_excerpt":"We study the concept of \\emph{compactor}, which may be seen as a counting-analogue of kernelization in counting parameterized complexity. For a function $F:\\Sigma^*\\to \\Bbb{N}$ and a parameterization $\\kappa: \\Sigma^*\\to \\Bbb{N}$, a compactor $({\\sf P},{\\sf M})$ consists of a polynomial-time computable function ${\\sf P}$, called \\emph{condenser}, and a computable function ${\\sf M}$, called \\emph{extractor}, such that $F={\\sf M}\\circ {\\sf P}$, and the condensing ${\\sf P}(x)$ of $x$ has length at most $s(\\kappa(x))$, for any input $x\\in \\Sigma^*.$ If $s$ is a polynomial function, then the compac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08160","kind":"arxiv","version":2},"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"}