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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 > p O(n/p) local comp. per round. Parallel Graph Algorithms. List Ranking. r-Ruling Set.

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Parallel Graph Algorithms

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  1. 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 > p O(n/p) local comp. per round Parallel Graph Algorithms

  2. List Ranking

  3. r-Ruling Set O(N/P) "selected" nodes with distance O(r) between consecutive nodes.

  4. 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.

  5. 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 > p • O(n/p) local comp. per round

  6. Det. List Ranking Algorithm • A CGM adaptation of deterministic coin tossing... CGM complexity: • O(log p) rounds • n/p > p • O(n/p) local comp. per round

  7. Rand. List Ranking

  8. Det. List Ranking

  9. 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

  10. Library Design

  11. Library Design

  12. Connected Components

  13. Bipartite Graph Detection

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