Daniel A. Spielman Research Overview

My research over the past decade has focused on problems at the intersection of Algorithms and Combinatorics with Optimization, Scientific Computation and Engineering. In my work, I develop mathematically rigorous analyses of algorithms and heuristics used to solve fundamental computational problems. I then try to use these analyses to obtain insight into how these problems can be better solved in practice. In this overview, I describe my work in the areas of Smoothed Analysis, Combinatorial Scientific Computing, and Error-Correcting Codes. My work on Error-Correcting Codes has led to four patents, and has been extended and applied many times. I have spent much of the Winter of 2005 implementing my latest combinatorial scientific algorithm: a solver for certain familes of linear equations. The experimental results we have obtained so far indicated that it may be the fastest solver for a large fragment of these families. We still do not know if Smoothed Analysis, the most ambitious and theoretical of my analyses, will lead to improvements in practice.