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How to reorder variables to produce a banded matrix of minimum bandwidth?

What is the time and space complexity of direct sparse solvers (e.g., UMFPACK, SUPERLU, PARDISO, etc.) for finite element matrices in 2D and 3D? How does the complexity splits into the creation of the inverse and the forward/backward substitution? Can anybody make some notes on this topic and/or post here some references?

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    $\begingroup$ This question was previously answered here: scicomp.stackexchange.com/a/868/67 $\endgroup$ – Jack Poulson May 15 '12 at 12:40
  • $\begingroup$ Good question, as @JackPoulson points out it's been previously answered. I'm going to leave this question closed so others can find their way to the good answers in the other question. Suggestions for improving the title/text of the other question for better searchability are welcome. $\endgroup$ – Aron Ahmadia May 15 '12 at 14:13