Excerpts from Intro to High Performance Computing
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Excerpts from Intro to High Performance Computing


You may have seen a recent news story of a
team of Japanese and German researchers who wrote a program to simulate the human brain. Brainsssssss. And in fact, their program didn’t simulate
the entire brain, just one percent of it. Now one percent of the brain is about 2 billion
neurons and 10 trillion synapses. Every synapse required about 24 bytes of storage. I think you can imagine that 24 bytes times
10 trillion is a lot of bytes. Now suppose I gave you a computer work station
with 16 gibibytes of main memory. Here’s my question to you. How many of these 16 gigibytes machine would
you need to store a full model that is all 100% of the brain? Now suppose the DAG[database availability
group] has work W(n) and span D(n). The ratio of work to span, or W divided by
D has a special interpretation. You basically measure the amount of work per
critical path vertex. So think about that for a second. At every critical path vertex, there’s average
amount of work. So this ratio basically tells you the average
available parallelism in the DAG. Remember, our original question was to get
an upper-bound, so can we get an upper-bound on some end? Now the floor of something is always less
than or equal to that something. Haha! That give an upper-bound and eliminates the
floor. “Oh no, I’m falling into a pit.” OK this looks a lot cleaner. Now you just need a little algebra and the
fact that summing all these Wk’s will give you W. Putting that all together you get your
first interesting result. Congratulations, this is Brent’s Theorem.

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