The normally used definition of speedup would be the run-time of the parallel algorithm executed on p processors/the run-time of the fastest known sequential algorithm. Comparing a parallel version of a program on p processors with that on 1 processor would be unfair since parallel programs are likely to gain performance due to its nature in design. However speedup against the parallel version on one core could be a measurement for reference since it might give us insight on the effect of tradeoffs we made in making the program parallel.
@zvonryan - I think the definition of speedup (as given in lecture 4, slide 4) is the amount of time taken to run the a program sequentially (on one processor) divided by the amount of time taken to run the program on p processors. I agree with you about it being unfair to compare parallel on core to multiple cores since a good parallel algorithm will scale with the number of processors