Past, Future and Cuts in Dataflow: Review
Answer these questions to review the webpage on past, future and
cuts in dataflow.
-
What is the concept of time in dataflow? What do before and after
mean in a dataflow graph?
-
What is a cut in a dataflow graph?
-
What is the relationship between a cut in a dataflow graph and a
cut in a flow network?
-
What is the state of a cut?
-
Draw a dataflow graph. Identify two or more cuts in the graph.
-
For the cuts in the previous example, give examples of dataflows
consisting only of
past
events, and only of
future
events.
-
For the cuts in the previous example, give examples of
computations in which
past
events precede
future
events.
-
Give an example of a partition of the set of vertices of a
dataflow graph into subsets
past
and
future
where a message from future
is
received in past
.
Explain why this partition is not a cut.
-
A property of a cut is that for each channel \(c\), the number of
messages sent on the channel in
past
is at least the
number of messages received on the channel.
Consider a partition (past, future)
of the set of vertices,
specified by a vector \(n\) where past
consists of
the first \(n[k]\) events of agent \(k\).
Is this partition necessarily a cut if the total number of
messages sent in past
is at least the total number of
messages received in past
?
Next
The properties of cuts in dataflow, and the concepts of before - after,
past - future are central for
algorithms by
which agents record the
states of distributed systems discussed in the next chapter.
K. Mani Chandy,
Emeritus Simon Ramo Professor,
California Institute of Technology