More Applications of the Polynomial Method to Algorithm Design

@inproceedings{Abboud2015MoreAO,
  title={More Applications of the Polynomial Method to Algorithm Design},
  author={Amir Abboud and Richard Ryan Williams and Huacheng Yu},
  booktitle={SODA},
  year={2015}
}
In low-depth circuit complexity, the polynomial method is a way to prove lower bounds by translating weak circuits into low-degree polynomials, then analyzing properties of these polynomials. Recently, this method found an application to algorithm design: Williams (STOC 2014) used it to compute all-pairs shortest paths in n3/2Ω([EQUATION]log n) time on dense n-node graphs. In this paper, we extend this methodology to solve a number of problems in combinatorial pattern matching and Boolean… 
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