26 Large Scale and Big Data
between two machines is dependent on their relative locations in the network topol-
ogy. For instance, machines that are on the same rack have higher bandwidth between
them as opposed to machines that are off-rack. As such, it pays to minimize network
trafc across racks. If P
1
, P
2
, and P
3
are mapped to M
1
, M
2
, and M
3
, respectively, less
network latency will be incurred when P
1
, P
2
, and P
3
communicate vs. if they are
mapped across the two racks. More precisely, for P
1
to communicate with P
2
on the
same rack, only one hop is incurred to route a message from P
1
to P
2
. In contrast, for
P
1
to communicate with P
2
on different racks, two hops are incurred per each mes-
sage. Clearly, a less number of hops results in a bet ...