Abstract
In parallel programming when a graph is distributed among processors it is useful to introduce consecutive local numeration of vertices for fast access to vertices and their adjacent vertices. The problem of mapping of global adjacency lists to local numeration arises. A graph can be distributed among processors after predecomposition or some vertices can be moved to other processors during partitioning. So vertex global numbers on a processor can be any and in any order. The algorithm devised in the parallel partitioning tool GridSpiderPar works with any local numeration, even with nonoptimal one. It can be applied to a whole graph or to a part of the graph. This algorithm allowed to reduce execution time of mapping of global adjacency lists to local numeration in a distributed graph in 18 times and the time of adding vertices to the graph while redistributing groups of bad subdomains – in 32 times on a tetrahedral mesh with 2·108 vertices. All these algorithms are parts of the parallel incremental algorithm for graph partitioning from the GridSpiderPar package. The proposed algorithm can also be used when some information about vertices is received from the other processors. It helps to find these vertices in the local graph faster. In common it replaces a sequence of searches in a large array with one looking through two sorted arrays for coincidences and can be applied in such algorithms.
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Golovchenko, E. (2023). An Algorithm for Mapping of Global Adjacency Lists to Local Numeration in a Distributed Graph in the GridSpiderPar Tool. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds) Supercomputing. RuSCDays 2023. Lecture Notes in Computer Science, vol 14389. Springer, Cham. https://doi.org/10.1007/978-3-031-49435-2_10
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