Distributed computing



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distcomp

MODEL

  • Links are bidirectional. A message traverses a single link.
  • All nodes have distinct ids. Each node knows immediate neighbors
  • Messages incur arbitrary but finite delay.
  • FIFO discipline on links, i.e., messages are received in the order they are sent.

PRELIMINARY: ESTABLISH A SPANNING TREE

  • Some node establishes itself as the leader (e.g. node x establishes a spanning tree for its broadcasts, so x is root).
  • That node sends out a “request for children” to its neighbors in the graph.
  • When a node n receives “request for children” from node m
  • if m is the first node that sent n this message, then n responds “ACK and you’re my parent”; sends request for children to its other neighbors else n responds “ACK”
  • Each node except the root has one parent, and every node is
  • in the tree. A leaf is a node that only received ACKs from
  • neighbors to which it sent requests.

TERMINATING THE SPANNING TREE

  • A node that determines that it is a leaf sends up an “I’m all done” message to its parent.
  • Each non-root parent sends an “I’m all done” message to its parent once it has received such message from all its children.
  • When the root receives “I’m all done” from its children, then it is done.

BROADCAST WITH FEEDBACK

  • A given node s would like to pass message X to all other nodes in the network and be informed that all nodes have received the message.
  • Algorithm:
  • Construct the spanning tree and then send X along the tree.
  • Have each node send an acknowledgement to its parent after it has received an acknowledgement from its children.

PROCESS TERMINATION

  • Def: Detect the completion of a collection of non-interacting tasks, each of which is performed on a distinct processor.
  • When a leaf finishes its computation, it sends an “I am terminated” message to its parent.
  • When an internal node completes it has received an “I am terminated” message from all of its children, it sends such a message to its parent.
  • When the root completes and has received an “I am terminated” message from all of its children, all tasks have been completed.
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