Parallel Graph Algorithms
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list ranking
connectivity
tree compression
bip. graph testing
max. matching in bip.
graph
• convexity of bip.
graphs (01-property)
• planarity testing
Frank Dehne
CGM complexity:
• O(log p) rounds
• n/p > p
• O(n/p) local comp. per
round
www.dehne.net
List Ranking
proc.1
Frank Dehne
proc.2
proc.3
proc.4
www.dehne.net
r-Ruling Set
O(N/P) "selected" nodes with distance O(r)
between consecutive nodes.
O(r)
Frank Dehne
O(r)
O(r)
O(r)
www.dehne.net
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.
Frank Dehne
www.dehne.net
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
Frank Dehne
www.dehne.net
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
Frank Dehne
www.dehne.net
Rand. List Ranking
Frank Dehne
www.dehne.net
Det. List Ranking
Frank Dehne
www.dehne.net
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
...
Frank Dehne
CGMlib
CGM utilities
CGMgraph
CGM graph algorithms
Download and
documentation at
http://cgm.dehne.net
www.dehne.net
Library Design
Frank Dehne
www.dehne.net
Library Design
Frank Dehne
www.dehne.net
Connected Components
Frank Dehne
www.dehne.net
Bipartite Graph Detection
Frank Dehne
www.dehne.net
Frank Dehne
www.dehne.net