Minimum Spanning Trees for Minor-Closed Graph Classes in Parallel
نویسنده
چکیده
For each minor-closed graph class we show that a simple variant of Borůvka’s algorithm computes a MST for any input graph belonging to that class with linear costs. Among minor-closed graph classes are e.g planar graphs, graphs of bounded genus, partial k-trees for fixed k, and linkless or knotless embedable graphs. The algorithm can be implemented on a CRCW PRAM to run in logarithmic time with a work load that is linear in the size of the graph. We develop a new technique to find multiple edges in such a graph that might have applications in other parallel reduction algorithms as well.
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