A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians

@inproceedings{Koutis2007ALW,
  title={A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians},
  author={Ioannis Koutis and Gary L. Miller},
  booktitle={SODA},
  year={2007}
}
We present a linear work parallel iterative algorithm for solving linear systems involving Laplacians of planar graphs. In particular, if <i>Ax</i> = <i>b</i>, where <i>A</i> is the Laplacian of any planar graph with <i>n</i> nodes, the algorithm produces a vector <i>x</i> such that ||<i>x</i>--<i>x</i>||<i>A</i> ≤ ε, in <i>O</i>(<i>n</i><sup>1/6+</sup><i>c</i>log(1/ε)) parallel time, doing <i>O</i>(<i>n</i>log(1/ε)) work, where <i>c</i> is any positive constant. One of the key ingredients of… CONTINUE READING

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