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Re:About the so-called SPFA algorithm
In Reply To:About the so-called SPFA algorithm Posted by:zhougelin at 2010-01-01 05:34:13
我懒得写中文版了。英文很烂，大家将就看吧。 顺祝新年快乐 :) > The formal academic reference can be found in the course "Network Optimization" of MIT. > You can achieve it using this link (SES #7, Page 18-20) : > http://ocw.mit.edu/OcwWeb/Sloan-School-of-Management/15-082JNetwork-OptimizationSpring2003/LectureNotes/index.htm > It is just an improvement of Bellman-Ford algorithm, and its worst case complexity is very bad. > Furthermore, it is very easy to construct a data to defeat this algorithm. > Suppose you want the shortest path from vertex 1 to vertex n, > then we can add edge (i, i + 1) with a small random weight for 1 <= i < n (thus the shortest path should be 1-2-...-n), > and randomly add 4n other heavy edges. For this case, the so-called SPFA algorithm will be very slow. > > > (1) SPFA is just a variation of Bellman-Ford, and SPFA is not its real name. > (2) It works well on random sparse graph, but programming contest should consider the worst case. > (3) Anyway, it is much faster than the original Bellman-Ford, > so it will be very helpful if we want to find the shortest path in graphs containing negative weight edges, > such as min cost flow problem.
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