Parallel Graph Algorithms

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Parallel Graph Algorithms

• list ranking
• connectivity
• tree compression
• bip. graph testing
• max. matching in bip. graph
• convexity of bip. graphs (01-property)
• planarity testing

• CGM complexity
• O(log p) rounds
• n/p gt p
• O(n/p) local comp. per round

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List Ranking
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r-Ruling Set

• O(N/P) "selected" nodes with distance O(r)
  between consecutive nodes.

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List Ranking Algorithm

• Determine an O(p2)-ruling set.
• Execute O(log p) rounds of pointer jumping.
• Compress ruling set into one processor and
  perform list ranking sequentially.
• Compute ranks of all other nodes.

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Rand. List Ranking Algorithm

• Select random n/p elements as ruling set and then
  improve ...
• CGM complexity
• O(log p log log n) rounds
• n/p gt p
• O(n/p) local comp. per round

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Det. List Ranking Algorithm

• A CGM adaptation of deterministic coin
  tossing...
• CGM complexity
• O(log p) rounds
• n/p gt p
• O(n/p) local comp. per round

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Rand. List Ranking
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Det. List Ranking
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CGM Graph Algorithm Library

• list ranking
• connectivity
• tree compression
• bip. graph testing
• max. matching in bip. graph
• convexity of bip. graphs (01-property)
• planarity testing
• ...

CGMlib CGM utilities CGMgraph CGM graph
algorithms Download and documentation at
http//cgm.dehne.net
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Library Design
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Library Design
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Connected Components
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Bipartite Graph Detection
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