12139

Parallel Computation of Functions on Set Partitions

Chetan Rokhade
San Diego State University
San Diego State University, 2014

@phdthesis{rokhade2014parallel,

   title={Parallel Computation of Functions on Set Partitions},

   author={Rokhade, Chetan},

   year={2014},

   school={San Diego State University}

}

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Many algorithms of practical interest require evaluation of a given function F on each point of a domain consisting of all k-partitions of an N-element set. Because the cardinality of such a domain grows rapidly for fixed k and increasing N, such algorithms are appealing candidates for parallelization; but to implement such parallelization efficiently in a multi-threaded (e.g., GPU/CUDA) architecture requires that each of Stirling2(N,k) threads determine — as a function of thread index alone, in time independent of the thread index, and without recourse to inter-thread communication — a unique corresponding k-partition of the given N-element set. While a number of sequential algorithms are known for recursively enumerating all k-partitions of an N-element set, none of those algorithms can be parallelized while satisfying the requirements above, since each requires that the mth k-partition in the enumeration be known before the (m+1)st k-partition can be computed. This thesis project comprised the design, coding, and testing of a parallel algorithm and corresponding CUDA implementation which do satisfy those requirements.
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