CS492 Special Topics in Computer Science:
Distributed Algorithms and Systems
Lecture #18
Distributed Algorithms (VI)
Admin Stuff
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Chapter 4
Algorithms in General
Synchronous Networks
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Minimum Spanning Tree (MST)
• Distributed algorithm for constructing an MST
in an arbitrary weighted undirected graph
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• At level 0
– components with individual nodes and no edges
• At level k
– each process knows the UID of the leader
– this UID is the identifier of the component
– each process also knows which of its incident
edges are in the component’s tree
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• At level k+1
– each level k component conducts a search along its
spanning tree edges for MWOE (minimum-weight
outgoing edge)
– among its incident edges, each process finds the one
with minimum weight that is outgoing from the
component; by sending test messages along all nontree edges, asking whether or not the other end is in
the same component
– then processes “convergecast” this local minimumweight edge toward the leader
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• Leader election at merger
– the new leader is the endpoint of the newly added
edge having the larger UID
– this new UID is broadcast to the entire component
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Complexity Analysis
• Number of levels?
• Time complexity?
• Communication complexity?
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Non-unique edge weights?
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Maximal Independent Set
• Definition:
– A set of nodes is called an independent set if it
contains no pair of neighboring nodes
– An independent set is maximal if it cannot be
increased to form a larger independent set by the
addition of any other nodes
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Motivation for MIS?
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Basic Idea
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Formal Statement of the Problem
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Randomized algorithms
• Benefits
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