Speedup is defined as the ratio between the time required by
the best serial algorithm to solve a given problem and the
time required by a parallel algorithm executing on p processors
to solve the same problem [17]. That is, given 
, the
time required by the serial algorithm, and 
, the time required
by the parallel algorithm on p processors, the speedup of
the parallel algorithm over the serial algorithm, 
,
is given by
Figure 14 shows the average speedup achieved while searching for terms related to the test queries using 2, 4, 8, 12, 16, 20, and 24 processors. Similarly, Figure 15 shows the average speedup while searching for documents related to the same queries. Again, memory constraints prevented testing a two-processor machine serving the USENET collection.
Since the PVM and PLMTP collections are fairly small, they both produced relatively flat speedup curves. Spreading their term and document vectors over increasing numbers of processors did not significantly decrease the time required to process queries in those collections. The CCE collection showed a slight speedup, although its curve appears to reach its asymptotic limit between 8 and 9 as the number of processors is increased. The USENET collection showed the most dramatic speedup of all the document collections. However, the super-linear speedup of plsiBackend on the USENET collection is due to the data being maintained in memory compared to the relatively inefficient way lsiBackend must load its data from disk incrementally.
