Abstract
Let G = (V, E) be a biconnected (2-edge connected), undirected graph with n vertices and m edges. A positive real weight is associated with every edge of the graph. Let d be the average depth, of a shortest path tree S G (s), rooted at s. Removal of a tree edge e = (u, v) (u is parent of v) breaks the shortest path tree into two parts, T 1—the subtree containing s and T 2—the sub tree rooted at v. For each tree edge e, we are required to find a non-tree edge, with one end point in T 1 and the other end point in T 2 such that the average distance from the root s to all the nodes in the disconnected subtree T 2 is minimised. The proposed parallel algorithm can be implemented on the Concurrent Read Exclusive Write (CREW) model either in (1) O((log m)3/2) time using O(m + nd + m(log m)1/2) operations (processor-time product), or alternatively in (2) O(log m) time using O(m + nd + m log m) operations.
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Kare, A.S., Saxena, S. (2014). Swap Edges of Shortest Path Tree in Parallel. In: Biswas, G., Mukhopadhyay, S. (eds) Recent Advances in Information Technology. Advances in Intelligent Systems and Computing, vol 266. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1856-2_9
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DOI: https://doi.org/10.1007/978-81-322-1856-2_9
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