Subquadratic time approximation algorithms for the girth

@inproceedings{Roditty2012SubquadraticTA,
  title={Subquadratic time approximation algorithms for the girth},
  author={Liam Roditty and Virginia Vassilevska Williams},
  booktitle={SODA},
  year={2012}
}
We study the problem of determining the girth of an unweighted undirected graph. We obtain several new efficient approximation algorithms for graphs with n nodes and m edges and unknown girth g. We consider additive and multiplicative approximations. Additive Approximations. We present: • an Õ(n/m)-time algorithm which returns a cycle of length at most g + 2 if g is even and g + 3 if g is odd. This complements the seminal work of Itai and Rodeh [SIAM J. Computing’78] who gave an algorithm that… CONTINUE READING