#
Time-Universal Data Compression^{ †}

^{1}

^{2}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. The Statement of the Problem and Preliminary Example

**Definition**

**1.**

**Comment**

**1**

**Comment**

**2**

## 3. The Time-Universal Code for the Finite Set of Data Compressors

#### 3.1. Theoretical Consideration

**Theorem**

**1.**

#### 3.2. Experiments

## 4. The Time-Universal Code for Stationary Ergodic Sources

**Theorem**

**2.**

## Funding

## Conflicts of Interest

## Appendix A

**Proof**

**of**

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**2.**

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$\mathbf{File}$ | Length (bites) | Best Compressor | Chosen Compressor | Chosen/Best (Ratio of Length) |
---|---|---|---|---|

BIB | 111,261 | nanozip | lpaq8 | 1.06 |

BOOK1 | 768,771 | nanozip | nanozip | 1 |

BOOK 2 | 610,856 | nanozip | nanozip | 1 |

GEO | 102,400 | nanozip | ccm | 1.07 |

NEWS | 377,109 | nanozip | nanozip | 1 |

OBJ1 | 21,504 | nanozip | tornado | 1.23 |

OBJ2 | 246,814 | nanozip | lpaq8 | 1.08 |

PAPER1 | 53,161 | nanozip | tornado | 1.52 |

PAPER2 | 82,199 | nanozip | tornado | 1.54 |

PIC | 513,216 | zpaq | bbb | 1.25 |

PROGC | 39,611 | nanozip | tornado | 1.42 |

PROGL | 71,646 | nanozip | tornado | 1.44 |

PROGP | 49,379 | lpaq8 | tornado | 1.4 |

TRANS | 93,695 | lpaq8 | lpaq8 | 1 |

$\mathbf{File}$ | Legth | Best Compressor | Chosen Compressor | Chosen/Best (Ratio of Length) |
---|---|---|---|---|

BIB | 111,261 | nanozip | nanozip | 1 |

BOOK1 | 768,771 | nanozip | nanozip | 1 |

BOOK 2 | 610,856 | nanozip | nanozip | 1 |

GEO | 102,400 | nanozip | nanozip | 1 |

NEWS | 377,109 | nanozip | lpq1v2 | 1.14 |

OBJ1 | 21,504 | nanozip | ccm | 1.17 |

OBJ2 | 246,814 | nanozip | nanozip | 1 |

PAPER1 | 53,161 | nanozip | lpaq8 | 1.19 |

PAPER2 | 82,199 | nanozip | nanozip | 1 |

PIC | 513,216 | zpaq | bbb | 1.25 |

PROGC | 39,611 | nanozip | lpaq8 | 1.04 |

PROGL | 71,646 | nanozip | lpaq8 | 1.03 |

PROGP | 49,379 | lpaq8 | lpaq8 | 1 |

TRANS | 93,695 | lpaq8 | lpaq8 | 1 |

Length of File (byte) | Number of Files | Ratio “Chosen Best” | Average “Worst/best” | Average “Chosen/Best” |
---|---|---|---|---|

≤${10}^{5}$ | 1496 | 8% | 112.87% | 103.57% |

${10}^{5}\u2013{10}^{6}$ | 1122 | 45.72% | 131.22% | 102.04% |

${10}^{6}\u2013{10}^{8}$ | 384 | 71% | 147.95% | 100.99% |

Length of File (byte) | Number of Files | Ratio “Chosen Best” | Average “Worst/Best” | Average “Chosen/Best” |
---|---|---|---|---|

≤${10}^{5}$ | 1496 | 16% | 112.87% | 102.14% |

${10}^{5}\u2013{10}^{6}$ | 1122 | 53.63% | 131.22% | 101.33% |

${10}^{6}\u2013{10}^{8}$ | 384 | 73% | 147.95% | 100.84% |

Length of File (byte) | Number of Files | Ratio “Chosen Best” | Average “Worst/Best” | Average “Chosen/Best” |
---|---|---|---|---|

≤${10}^{5}$ | 1496 | 14% | 112.87% | 102.48% |

${10}^{5}\u2013{10}^{6}$ | 1122 | 54.9% | 131.22% | 101.92% |

${10}^{6}\u2013{10}^{8}$ | 384 | 73% | 147.95% | 100.86% |

Length of File (byte) | Number of Files | Ratio “Chosen Best” | Average “Worst/Best” | Average “Chosen/Best” |
---|---|---|---|---|

≤${10}^{5}$ | 1496 | 10% | 112.87% | 103.12% |

${10}^{5}\u2013{10}^{6}$ | 1122 | 44.69% | 131.22% | 102.54% |

${10}^{6}\u2013{10}^{8}$ | 384 | 72% | 147.95% | 100.88% |

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**MDPI and ACS Style**

Ryabko, B. Time-Universal Data Compression. *Algorithms* **2019**, *12*, 116.
https://doi.org/10.3390/a12060116

**AMA Style**

Ryabko B. Time-Universal Data Compression. *Algorithms*. 2019; 12(6):116.
https://doi.org/10.3390/a12060116

**Chicago/Turabian Style**

Ryabko, Boris. 2019. "Time-Universal Data Compression" *Algorithms* 12, no. 6: 116.
https://doi.org/10.3390/a12060116