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Ordering for <strong>Sparse</strong> Cholesky (2/2, cont.)<br />
Generalized nested dissection [Lipton/Rose/Tarjan ’79]<br />
Global graph partitioning: top-down, divide-and-conqure<br />
First level<br />
Recurse on A and B<br />
Goal: find the smallest possible separator S at each level<br />
Multilevel schemes:<br />
A S B<br />
⎡ A 0 x ⎤<br />
⎢<br />
⎥<br />
⎢<br />
0 B x<br />
⎥<br />
⎢⎣<br />
x x S ⎥⎦<br />
Chaco [Hendrickson/Leland `94], Metis [Karypis/Kumar `95]<br />
Spectral bisection [Simon et al. `90-`95]<br />
Geometric and spectral bisection [Chan/Gilbert/Teng `94]<br />
X. Li<br />
14
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