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    DC-RST: a highly parallel, divide-and-conquer algorithm for creating random spanning trees on a clique

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    Author
    Henke, Lucas R.
    Advisor
    Mehta, Dinesh P.
    Date issued
    2021
    Keywords
    Dimecost
    divide and conquer
    Mantel test
    network analytics
    parallel
    Wilson's algorithm
    
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    URI
    https://hdl.handle.net/11124/14293
    Abstract
    We describe DC-RST, a highly parallel, divide and conquer algorithm for generating a random spanning tree of a complete graph on $n$ vertices such that each edge in the graph is chosen with equal probability. DC-RST parallelizes Wilson's sequential random-walk algorithm which has an expected complexity of $\Theta(n)$ on a complete graph. On a system with 48 cores, on some instances, DC-RST was up to 4X faster when first creating random partitions and up to 20X faster without this sub-step. Although the spanning trees generated by DC-RST are random, unlike those generated by Wilson's algorithm, they are not \textit{uniform} random spanning trees. The proposed application of DC-RST is network analytics, where we seek to determine whether two distance metrics on a graph with $n$ entities are statistically correlated. DC-RST utilizes parallelization to speed up \textsc{DimeCost}, a sequential linear-time algorithm based on uniform random spanning trees. Although DC-RST does not create \textit{uniform} random spanning trees, our preliminary statistical testing comparing it with \textsc{DimeCost}, indicates that results obtained by DC-RST are reliable.
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