In an undergrad class on linear programming, we learned about the simplex and ellipsoid methods for solving linear programs (LPs). I know that the simplex method is generally faster than the ellipsoid method, but its worst-case complexity is much slower. In searching the web and the book we used I haven't been able to find much beyond that summary.
Can anyone give me a situation in which the simplex method devolves into an exponential running time, which would make it slower than the ellipsoid method? An example of an actual LP would be awesome, but any info is greatly appreciated.
Also, please let me know if this is not the right SE for this specific question. I didn't see much at all on the ellipsoid method when searching before posting this question.