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# Class Note for EECS 560 with Professor Huan at KU (2)

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COURSE
PROF.
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TYPE
Class Notes
PAGES
2
WORDS
KARMA
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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 25 views.

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Date Created: 02/06/15
Relax operation du the distance from the source to the node u getting updated during single source shortest path computation 11u the parent of u for trace back Wvu the edge weight from V to u if there is no edge the weight is positive in nity 5u is the shortest distance from source to the node u Relax u V If du gt dv wvu du dv wv u 11u V Bellman ford algorithm for graphs with negatively weighted edges Single source shortest path G s For each u e V du positive infinity ds 0 ForI l V For each u v e E Relaxuv Dijkstra39s Algorithms S lt 0 T lt VG initialize a priority queue While Qi 0 u lt extract MinQ S lt S U u for each V e Adj u relaxuvw if we use array to implement Dijkstra s algorithms Initialize V extract Min V V relax 1E Therefore OVVVEOV2 Use minheap V lgVV lgVE Therefore OVV1g V E 1g V OE 1g V using Fibonacci heap OE V 1g V All Pairs Sh01test Path Johnson39s Algorithm Johnson s algorithm contains three steps 1 For a graph G construct a new graph G with an additional node U and create directed edges from U to each and every node in G with weight 0 2 Compute the weight potential of the nodes in G where the weight The weight of a node X hX is the shortest distance from U to X 3 Update the weight of each edge W W with the following formula W uv hll39hV W uv Claims 1 ifuV ifthe shortest path is G uV ifthe shortest path is C 2 W W 2 0 Implementation Run Bellmanford algorithm VVE to obtain the potential of each node Run Dijkstra s algorithm V times to obtain all pair shortest distance Total running time V E 1g V

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