Distributed Algorithms Contents Index

Past, Future and Cuts in Dataflow: Review

Answer these questions to review the webpage on past, future and cuts in dataflow.
  1. What is the concept of time in dataflow? What do before and after mean in a dataflow graph?
  2. What is a cut in a dataflow graph?
  3. What is the relationship between a cut in a dataflow graph and a cut in a flow network?
  4. What is the state of a cut?
  5. Draw a dataflow graph. Identify two or more cuts in the graph.
  6. For the cuts in the previous example, give examples of dataflows consisting only of past events, and only of future events.
  7. For the cuts in the previous example, give examples of computations in which past events precede future events.
  8. 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.
  9. 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?
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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