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Discrete Mathematics & Theoretical Computer Science |
In this paper, we study the shuffle operator on concurrent processes (represented as trees) using analytic combinatorics tools. As a first result, we show that the mean width of shuffle trees is exponentially smaller than the worst case upper-bound. We also study the expected size (in total number of nodes) of shuffle trees. We notice, rather unexpectedly, that only a small ratio of all nodes do not belong to the last two levels. We also provide a precise characterization of what ``exponential growth'' means in the case of the shuffle on trees. Two practical outcomes of our quantitative study are presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random generation of concurrent runs.
Source : ScholeXplorer
IsRelatedTo ARXIV 0802.2844 Source : ScholeXplorer IsRelatedTo DOI 10.4230/lipics.stacs.2008.1317 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.0802.2844
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