Space Speedup and Its Relationship with Time Speedup

In the optimizing work of parallel program, especially in the realm of massively parallel computing, the parallel computing time and space must be concurrently carefully considered to cut down the computing time as much as possible, because lots of poor parallel space strategies would impact negative effects on computing time. Although, sometimes we have no choice but to sacrifice the space for the time´s further diminishing. What relationship should the computing time and space to keep and how are they going on are two problems, which deciding our optimizing direction directly and must be clear in parallel optimizing. This paper proposes a space theory, named as space speedup, to denote the scalability of memory requirement, and discusses the relationship of time speedup and space speedup, through which the speedups´ guidance capacity in optimizing parallel codes are given.