Large deviations for increasing subsequences of permutations and a concurrency application

Yuliy Baryshnikov, Abram Magner

研究成果: Contribution to journalConference article


The study of concurrent processes with conflicts aecting concurrent execution has been long related to various geometric objects. In the special case of two processes and non-overlapping conflicts (definitions below) an instance of a problem is encoded by a permutation describing the conflict sets for the interacting processes. Further, it turns out that the set of increasing subsequences of the permutation describes the homotopy classes of the execution plans for the concurrent processes, an abstraction encoding one particular serialization of the executions of two processes. This motivates the study of random increasing subsequences of random permutations. Here, we give a large deviation principle which implies that such a subsequence never deviates too far from the identity permutation: a random serialization of two concurrent processes will not delay either process's access to shared resources too much at any given time. We then give an efficient exact algorithm for uniform random sampling of an increasing subsequence from a given permutation. Finally, we indicate how our results generalize to larger numbers of processes, wherein conflict sets may take on more interesting geometries.

ジャーナルPerformance Evaluation Review
出版物ステータス出版済み - 3 20 2018
イベント35th IFIP International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIP WG 7.3 Performance 2017 - New York, 米国
継続期間: 11 13 201711 17 2017

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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