A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs
Computational Complexity
2008-12-19 v1 Combinatorics
Abstract
Consider the problem of determining whether there exists a spanning hypertree in a given k-uniform hypergraph. This problem is trivially in P for k=2, and is NP-complete for k>= 4, whereas for k=3, there exists a polynomial-time algorithm based on Lovasz' theory of polymatroid matching. Here we give a completely different, randomized polynomial-time algorithm in the case k=3. The main ingredients are a Pfaffian formula by Vaintrob and one of the authors (G.M.) for a polynomial that enumerates spanning hypertrees with some signs, and a lemma on the number of roots of polynomials over a finite field.
Cite
@article{arxiv.0812.3593,
title = {A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs},
author = {Sergio Caracciolo and Gregor Masbaum and Alan D. Sokal and Andrea Sportiello},
journal= {arXiv preprint arXiv:0812.3593},
year = {2008}
}
Comments
6 pages, 1 figure