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Fig. 4. This graph displays the relative results of our experiments when we follow a
three tasks per worker splitting rule. During the experiments, we incrementally per-
form upgrades on a subset of the cluster. On the X-axis is the number of matrices
multiplied during the experiment. On the Y-axis is the execution time in seconds of
the MapReduce job relative to the time it took on the un-upgraded cluster.
improvements as smaller sections of the cluster are upgraded. This indicates
that further increasing the number of tasks will likely have a more dramatic
impact on turnaround time for these smaller percentage upgrade scenarios. This
is something we consider in the next section.
Note that in the data presented thus far our cluster is not heterogeneous
enough, nor the task granularity small enough, to see an improvement in per-
formance using the configurations presented. The reason we have not yet seen
performance improvements in most upgrade scenarios tested is because the
upgraded nodes are not fast enough as to be able to take over the execution
of all additional tasks that would be assigned to the stock (original) nodes when
assuming all nodes will process the same number of tasks.
5.3 Finer-Grained Splits
Figure 5 plots data for the same set of tests as Fig. 1 , for the finest granularity
of the initial data split. This provides the most potential for Faster nodes to
complete initial small assignments quickly and then retrieve more data and exe-
cute more tasks than slower nodes. In this case the Baseline homogeneous cluster
(0 % Faster nodes) performs worst across all problem sizes, and the Faster homo-
geneous (100 % Faster) cluster performs best, two unsurprising results. The other
three clusters, however, perform very similarly to one another across all problem
sizes, despite the disparity between the number of upgraded nodes.
 
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