Hedayati Somarin, Iraj
(2016)
*DFA Minimization Algorithms in Map-Reduce.*
Masters thesis, Concordia University.

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## Abstract

Map-Reduce has been a highly popular parallel-distributed programming model. In this thesis, we study the problem of minimizing Deterministic Finite State Automata (DFA). We focus our attention on two well-known (serial) algorithms, namely the algorithms of Moore (1956) and of Hopcroft (1971). The central cost-parameter in Map-Reduce is that of communication cost i.e., the amount of data that has to be communicated between the processes. Using techniques from Communication Complexity we derive an O(kn log{n}) lower bound and O(kn^3 log{n}) upper bound for the problem, where n is the number of states in the DFA to be minimized,and k is the size of its alphabet. We then develop Map-Reduce versions of both Moore's and Hopcroft's algorithms, and show that their communication cost is O(kn^2 (log {n} + log {k})). Both methods have been implemented and tested on large DFA, with 131,072 states. The experiments verify our theoretical analysis, and also reveal that Hopcroft's algorithm -- considered superior in the sequential framework -- is very sensitive to skew in the topology of the graph of the DFA, whereas Moore's algorithm handles skew without major efficiency loss.

Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering |
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Item Type: | Thesis (Masters) |

Authors: | Hedayati Somarin, Iraj |

Institution: | Concordia University |

Degree Name: | M. Comp. Sc. |

Program: | Computer Science |

Date: | 17 January 2016 |

Thesis Supervisor(s): | Grahne, Gösta K. |

Keywords: | Map-Reduce, Big-Data, Hadoop, Automata, DFA Minimization, Communication Complexity, Parallel, Distributed, Complexity Model |

ID Code: | 980838 |

Deposited By: | HEDAYATISOMARIN IRAJ |

Deposited On: | 16 Jun 2016 14:40 |

Last Modified: | 18 Jan 2018 17:52 |

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