From: MapReduce particle filtering with exact resampling and deterministic runtime

Section | Algorithmic component | Time | Space | Data transfers |
---|---|---|---|---|

4.1 | Element-wise operations | \({\mathcal {O}} (1)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (1)\) |

4.2 | Rotation | \({\mathcal {O}} (1)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (1)\) |

4.3 | Sum/max/min | \({\mathcal {O}} \left (\frac {N}{P}\log N\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}}(P)\) |

4.4 | Cumulative sum | \({\mathcal {O}} \left (\frac {N}{P}\log N\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}}(P)\) |

4.5 | Normalising the weights | \({\mathcal {O}} \left (\frac {N}{P}\log N\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}}{(P)}\) |

4.6 | Minimum variance resampling | \({\mathcal {O}} \left (\frac {N}{P}\log N\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}}(P)\) |

4.7 | (Bitonic) sort | \({\mathcal {O}} \left (\frac {N}{P}(\log N)^{2}\right)\) | \({\mathcal {O}}{(N)}\) | \({\mathcal {O}}(P)\) |

4.8.1 | Redistribution from [9] | \({\mathcal {O}} \left (\frac {N}{P}(\log N)^{3}\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (P)\) |

4.8.2 | Improved redistribution | \({\mathcal {O}} \left (\frac {N}{P}(\log N)^{2}\right)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (P)\) |

6.1.1 | Naïve redistribution | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (N)\) | \({\mathcal {O}} (1)\) |