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I/OEfficient Strong Connectivity and DepthFirst Searchfor Directed Planar Graphs
"... We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2/3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N ..."
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We present the first I/Oefficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simplepath 2/3separator, and computing a depthfirst spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E andsort(N) = \Theta ((N /B) logM/B(N/B)) is the number of I/Os required to sort N elements. The DFSalgorithm performs O(sort(N) log(N/M)) I/Os, where M is the number of elements that fit into main memory.
Efficient Parallel Algorithms for Planar stGraphs
, 2003
"... Planar stgraphs find applications in a number of areas. In this paper we present efficient parallel algorithms for solving several fundamental problems on planar stgraphs. The problems we consider include allpairs shortest paths in weighted planar stgraphs, singlesource shortest paths in weigh ..."
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Planar stgraphs find applications in a number of areas. In this paper we present efficient parallel algorithms for solving several fundamental problems on planar stgraphs. The problems we consider include allpairs shortest paths in weighted planar stgraphs, singlesource shortest paths in weighted planar layered digraphs (which can be reduced to singlesource shortest paths in certain special planar stgraphs), and depthfirst search in planar stgraphs. Our parallel shortest path techniques exploit the specific geometric and graphic structures of planar stgraphs, and involve schemes for partitioning planar stgraphs into subgraphs in a way that ensures that the resulting path length matrices have a monotonicity property [1], [2]. The parallel algorithms we obtain are a considerable improvement over the previously best known solutions (when they are applied to these stgraph problems), and are in fact relatively simple. The parallel computational models we use are the CREW PRAM and EREW PRAM.