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5 However, we show in Section 2.6.7 that two passes of MapReduce are usually better than one for matrix multiplica-
tion.
6 This algorithm uses much too much communication, but it will serve as a simple example of the Pregel computation
model.
7 Recall that this figure represented functions, not tasks. As a network of tasks, there would be, for example, many tasks
implementing function f , each of which feeds data to each of the tasks for function g and each of the tasks for function
i .
8 This person, or more generally, people with large extended circles of friends, are good people to use to start a market-
ing campaign by giving them free samples.
9 In a typical cluster, there are many switches connecting subsets of the compute nodes, so all the data does not need to
go across a single gigabit switch. However, the total available communication is still small enough that it is not feas-
ible to implement this algorithm for the scale of data we have hypothesized.
10 If q is less than 2 n , then a reducer cannot get even one row and one column, and therefore cannot compute any out-
puts at all.
11 Bit strings have Hamming distance 1 if they differ in exactly one bit position. You may look ahead to Section 3.5.6
for the general definition.
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