If networked people are faster solving problems than one, does the same apply to computers? Are there necessary constraints for this problem? Is there any benefit to knowing the answer to this question?
It all depends on the parallelisation algorithm, and how good it is. Whether the task is split across different computers on a network, or different CPU's it still comes down to whether or not your task is capable of being split into parallel computing streams. Some tasks are essentially serial, where each operation depends on the result of a previous operation for its input, so there is no benefit.
This article might help:
http://web.eecs.umich.edu/~qstout/parallel.html
Mark,
Thank you for your helpful comments and the article. I've read the article; it is is very on point, thank you.
Bob Shour
Ivor Catt did a lot of work on this when he developed the wafer scale integration supercomputers in the 1970's and 80's.
Working from memory I recall he demonstrated that pipelining effects significantly improved the throughput vs overhead ratio as the number of processors increased.
Although the fabrication technology of the time wasn't ready for this, I believe there is renewed spend and effort to revive these ideas.
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