An algebraic algorithm for weighted linear matroid intersection

@inproceedings{Harvey2007AnAA,
title={An algebraic algorithm for weighted linear matroid intersection},
author={Nicholas J. A. Harvey},
booktitle={SODA},
year={2007}
}

We present a new algebraic algorithm for the classical problem of weighted matroid intersection. This problem generalizes numerous well-known problems, such as bipartite matching, network flow, etc. Our algorithm has running time Õ(<i>nr</i><sup>ω-1</sup><i>W</i>1+ε) for linear matroids with <i>n</i> elements and rank <i>r</i>, where ω is the matrix multiplication exponent, and <i>W</i> denotes the maximum weight of any element. This algorithm is the fastest known when <i>W</i> is small. Our… CONTINUE READING