Suppose a program must execute 10 12 instructions in order to solve a problem Suppose a single processor can execute 10 6 instructions per second How many days will it take the single processor to solve the problem Now suppose we modify the program to run on a distributed memory system with p 1000 processors in such a way that each processor will execute 10 12 p instructions and send 10 9 (p 1) messages How long will it take to solve the problem if messages take 10 9 s to send How about if messages take 10 3 s to send Assume the program completes as soon as it has executed its instructions and sent its messages and that any other overhead is negligible How does the result change if we now assume a single processor can execute 10 9 operations per second What does this tell you about the tradeoff between computation and communication costs Give three examples of what might be considered as overhead

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Question: Suppose a program must execute 10 12 instructions in order to solve a problem. Suppose a single processor can execute 10 6 instructions per second.

Suppose a program must execute 10¹² instructions in order to solve a problem. Suppose a single processor can execute 10⁶ instructions per second.

How many days will it take the single processor to solve the problem?

Now suppose we modify the program to run on a distributed-memory system with p = 1000 processors in such a way that each processor will execute 10¹²/p instructions and send 10⁹ (p 1) messages.

How long will it take to solve the problem if messages take 10⁹ s to send?

How about if messages take 10³ s to send?

Assume the program completes as soon as it has executed its instructions and sent its messages and that any other overhead is negligible.

How does the result change if we now assume a single processor can execute 10⁹ operations per second?

What does this tell you about the tradeoff between computation and communication costs?

Give three examples of what might be considered as overhead.

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