Faster Algebraic Algorithms for Path and Packing Problems

@inproceedings{Koutis2008FasterAA,
  title={Faster Algebraic Algorithms for Path and Packing Problems},
  author={Ioannis Koutis},
  booktitle={ICALP},
  year={2008}
}
We study the problem of deciding whether an n-variate polynomial, presented as an arithmetic circuit G, contains a degree k square-free term with an odd coefficient. We show that if G can be evaluated over the integers modulo 2 in time t and space s, the problem can be decided with constant probability in O((kn+ t)2) time and O(kn+s) space. Based on this, we present new and faster algorithms for two well studied problems: (i) an O∗(2mk) algorithm for the m-set k-packing problem and (ii) an O… CONTINUE READING
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