This paper presents fast parallel algorithms for the following graph theoretic problems: breadth-depth search of directed acyclic graphs; minimum-depth search of graphs; finding the minimum-weighted paths between all ...
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This paper presents fast parallel algorithms for the following graph theoretic problems: breadth-depth search of directed acyclic graphs; minimum-depth search of graphs; finding the minimum-weighted paths between all node-pairs of a weighted graph and the critical activities of an activity-on-edge network. The first algorithm hasO(logdlogn) time complexity withO(n 3) processors and the remaining algorithms achieveO(logd loglogn) time bound withO(n 2[n/loglogn]) processors, whered is the diameter of the graph or the directed acyclic graph (which also represents an activity-on-edge network) withn nodes. These algorithms work on an unbounded shared memory model of the single instruction stream, multiple data stream computer that allows both read and write conflicts.
Two graph search problems are considered in a parallel computational environment. In this paper, we use the shortest path algorithm as a useful parallel computational technique. Based on the parallel shortest path alg...
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Two graph search problems are considered in a parallel computational environment. In this paper, we use the shortest path algorithm as a useful parallel computational technique. Based on the parallel shortest path algorithm presented by Dekel [8], we develop a parallel breadth first search algorithm for general graphs and a parallel depth first search algorithm for acyclic digraphs which run in timeO(logd-logn) using0(n2[n/logn]) *** a breadth first search, the resulting algorithm is the same with that of Ghosh and Bhattacharjee [9]. But the difference between them is that the algorithm presented in [9] is based on the parallel breadth first search algorithm for trees while our algorithm is based on the shortest path algorithm. Furthermore, the algorithms presented in this paper have a unified algorithm structure.
Parallel algorithms for analyzing activity networks are proposed which include feasibility test, topological ordering of the events, and computing the earliest and latest start times for all activities and hence ident...
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Parallel algorithms for analyzing activity networks are proposed which include feasibility test, topological ordering of the events, and computing the earliest and latest start times for all activities and hence identification of the critical activities of the activity network. The first two algorithms haveO(logn) time complexity and the remaining one achievesO(logd log logn) time bound, whered is the diameter of the digraph representing the activity network withn nodes. All these algorithms work on a CRCW PRAM and requireO(n 3) processors.
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