{"paper":{"title":"Families with infants: speeding up algorithms for NP-hard problems using FFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexander Golovnev, Alexander S. Kulikov, Ivan Mihajlin","submitted_at":"2014-10-08T18:27:38Z","abstract_excerpt":"Assume that a group of people is going to an excursion and our task is to seat them into buses with several constraints each saying that a pair of people does not want to see each other in the same bus. This is a well-known coloring problem and it can be solved in $O^*(2^n)$ time by the inclusion-exclusion principle as shown by Bj\\\"{o}rklund, Husfeldt, and Koivisto in 2009.Another approach to solve this problem in $O^*(2^n)$ time is to use the fast Fourier transform. A graph is $k$-colorable if and only if the $k$-th power of a polynomial containing a monomial $\\prod_{i=1}^n x_i^{[i \\in I]}$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2209","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"}