Parallel algorithms for labeling image components
Based on the CRCW PRAM (Concurrent-Read Concurrent-Write Parallel Random Access Machine) model, we show that Θ(N/logN) processors are necessary and sufficient to solve the image component problem in O(logN) time. The best known algorithm uses N processors to achieve the same time bound.
We show that Θ(N/log2N) hypercube or shuffle processors are necessary and sufficient to solve the same problem in O(log2N) time. This new result improves the processor requirement of the best existing algorithm by a factor of O(log2N).
We present a new mesh computer algorithm aimed to improve the utilization of the processor resource while maintaining reasonable speedup over the sequential algorithm. The algorithm that is presented uses only O(N1/2) processors and executes in O(N1/2logN) time. This time complexity is a factor of O(logN) away from the optimal time complexity of O(N1/2); however, the number of processors is reduced by a factor of O(N1/2) from O(N).
We show that these algorithms can be extended to compute components in k-dimension and to compute components based on generalized connectivities.
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