Enumeration and Random Generation of Concurrent Computations

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 o...

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AQ,...; no. Proceedings; pp. 83 - 96
Main Authors:	Bodini, Olivier, Genitrini, Antoine, Peschanski, Frédéric
Format:	Journal Article Conference Proceeding
Language:	English
Published:	DMTCS 01.01.2012 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science
Series:	DMTCS Proceedings
Subjects:	[info.info-cg] computer science [cs]/computational geometry [cs.cg] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [math.math-co] mathematics [math]/combinatorics [math.co] Combinatorics Computational Geometry Computer Science concurrency theory. analytic combinatorics. shuffle. random generation. linear extension Data Structures and Algorithms Discrete Mathematics Mathematics Concurrency theory. Analytic combinatorics. Shuffle. Random generation. Linear extension
ISSN:	1365-8050, 1462-7264, 1365-8050
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Summary:	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.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.2986