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Dijkstra's Algorithm
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When this parameter is supplied, the implementation will use the Eager Dijkstra's algorithm with the given lookahead value. Lookahead permits distributed Dijkstra's algorithm to speculatively process vertices whose shortest distance from the source may not have been found yet. When the distance found is the shortest distance, parallelism is improved and the algorithm may terminate more quickly. However, if the distance is not the shortest distance, the vertex will need to be reprocessed later, resulting in more work.
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From a purely technical point of view Dijkstra's Algorithm can be described as an iterative procedure inspired by (6) that repeatedly attempts to improve an initial approximation {F(j)} of the (exact) values of {f(j)}. The initial approximation is simply F(1)=0 and F(j)=infinity for j=2,...,n. The details are as follows.
Paul E. Black, "Dijkstra's algorithm", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 20 September 2006. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/dijkstraalgo.html
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The performance of the eager Dijkstra's algorithm varies greatly depending on the lookahead value. The following charts illustrate the performance of the Parallel BGL on graphs with edge weights uniformly selected from the range [0, 1) and a constant lookahead of 0.1.
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