### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 84-89 |

Number of pages | 6 |

Journal | Performance Evaluation Review |

Volume | 45 |

Issue number | 3 |

DOIs | |

State | Published - Mar 20 2018 |

Event | 35th IFIP International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIP WG 7.3 Performance 2017 - New York, United States Duration: Nov 13 2017 → Nov 17 2017 |

### Fingerprint

### Keywords

- Increasing subsequences
- Large deviations
- Permutations

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications

### Cite this

**Large deviations for increasing subsequences of permutations and a concurrency application.** / Baryshnikov, Yuliy; Magner, Abram.

Research output: Contribution to journal › Conference article

*Performance Evaluation Review*, vol. 45, no. 3, pp. 84-89. https://doi.org/10.1145/3199524.3199538

}

TY - JOUR

T1 - Large deviations for increasing subsequences of permutations and a concurrency application

AU - Baryshnikov, Yuliy

AU - Magner, Abram

PY - 2018/3/20

Y1 - 2018/3/20

N2 - 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.

AB - 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.

KW - Increasing subsequences

KW - Large deviations

KW - Permutations

UR - http://www.scopus.com/inward/record.url?scp=85046630092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046630092&partnerID=8YFLogxK

U2 - 10.1145/3199524.3199538

DO - 10.1145/3199524.3199538

M3 - Conference article

AN - SCOPUS:85046630092

VL - 45

SP - 84

EP - 89

JO - Performance Evaluation Review

JF - Performance Evaluation Review

SN - 0163-5999

IS - 3

ER -