Abstract
We present an associative algorithm for finding the second simple shortest paths from the source vertex to other vertices of a directed weighted graph. Our model of computation (the STAR-machine) simulates the run of associative (content addressable) parallel systems of the SIMD type with vertical processing. We first propose the data structure that uses the graph representation as a list of triples (edge end-points and the weight) and the shortest paths tree obtained by means of the classical Dijkstra algorithm. The associative algorithm is given as the procedure SecondPaths, whose correctness is proved and the time complexity is evaluated.
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