Chapter 7 (continued)

4. Karp-Flatt metric

   • This metric (see Section 7.5) gives you e, the "experimentally determined serial fraction" for a parallel application, where e is defined as:

        serial time + parallel overhead
        -------------------------------
            time on one processor
       

   • The metric is helpful in two ways:

     1. It gives an easy way to measure e, requiring only that you measure speedup for several values of p. This is often easier than figuring out exactly what f is in Amdahl's law.

     2. Since it includes both serial time and parallel overhead, one can sometimes see which one is to be blamed for poor parallel performance. Basically, if e grows with p, then that can be blamed on overhead rather than inherently sequential work. See Examples 1 and 2 on page 169.

5. Isoefficiency

   • Recall that increasing the problem size often improves parallel speedup (for a given number of processors p).

   • The isoefficiency metric asks this question: "as I increase the number of processors, by how much do I have to increase the total problem size in order to maintain a given parallel efficiency?"

   • If problem size has to grow at a rate no faster than the number of processors, then the application is perfectly scalable according to this metric. In this situation, the problem size per processor would remain bounded.

   • But if the problem size has to grow faster than the number of processors, then the application is not scalable. In this situation, eventually the problem size per processor gets too large.