### Abstract

The study of concurrent processes with conflict points is connected with the geometry of increasing subsequences of permutations - a permutation encodes the transactions of two processes that conflict (i.e., must be executed serially), and a given increasing subsequence encodes 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 favor either process 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.

Original language | English (US) |
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Pages (from-to) | 39-41 |

Number of pages | 3 |

Journal | Performance Evaluation Review |

Volume | 45 |

Issue number | 2 |

DOIs | |

State | Published - Sep 1 2017 |

Event | Workshop on MAthematical Performance Modeling and Analysis, MAMA 2017, 2017 Greenmetrics Workshop and Workshop on Critical Infrastructure Network Security, CINS 2017 - Urbana-Champaign, United States Duration: Jun 1 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. 2, pp. 39-41. https://doi.org/10.1145/3152042.3152056

}

TY - JOUR

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

AU - Baryshnikov, Yuliy

AU - Magner, Abram

PY - 2017/9/1

Y1 - 2017/9/1

N2 - The study of concurrent processes with conflict points is connected with the geometry of increasing subsequences of permutations - a permutation encodes the transactions of two processes that conflict (i.e., must be executed serially), and a given increasing subsequence encodes 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 favor either process 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.

AB - The study of concurrent processes with conflict points is connected with the geometry of increasing subsequences of permutations - a permutation encodes the transactions of two processes that conflict (i.e., must be executed serially), and a given increasing subsequence encodes 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 favor either process 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.

KW - Increasing subsequences

KW - Large deviations

KW - Permutations

UR - http://www.scopus.com/inward/record.url?scp=85041394574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041394574&partnerID=8YFLogxK

U2 - 10.1145/3152042.3152056

DO - 10.1145/3152042.3152056

M3 - Conference article

AN - SCOPUS:85041394574

VL - 45

SP - 39

EP - 41

JO - Performance Evaluation Review

JF - Performance Evaluation Review

SN - 0163-5999

IS - 2

ER -