A Parallel Algorithm for Finding All Successive Minimal Maximum Subsequences

Efficient algorithms for finding multiple contiguous subsequences of a real-valued sequence having large cumulative sums, in addition to its combinatorial appeal, have widely varying applications such as in textual information retrieval and bioinformatics. A maximum contiguous subsequence of a real-valued sequence is a contiguous subsequence with the maximum cumulative sum. A minimal maximum contiguous subsequence is a minimal contiguous subsequence (with respect to subsequential containment) among all maximum ones of the sequence. We present a logarithmic-time and optimal linear-work parallel algorithm on the parallel random access machine model that finds all successive minimal maximum subsequences of a real-valued sequence.

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