### Abstract

Combinations of n objects taken m at the time are ubiquitous in a wide range of combinatorial problems. In this paper, we introduce a novel approach to generate combinations from given integer numbers by using a gradient-based algorithm through plural number of CPU and GPU processors. The time complexity is bounded by O(m^{2}) when using a single processor, and bounded by O(mlog m) when using at most O(m/ log m) processors. Relevant computational experiments confirmed the practical efficiency within computationally allowable limits. Our approach offers the building blocks to represent combinations with succinct encoding and complexity being independent of n, which is meritorious when n is very large, or when n is time-varying.

Original language | English |
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Title of host publication | Internet and Distributed Computing Systems - 11th International Conference, IDCS 2018, Proceedings |

Editors | Antonio Guerrieri, Jason J. Jung, Giancarlo Fortino, Jingtao Sun, Yang Xiang |

Publisher | Springer-Verlag |

Pages | 16-26 |

Number of pages | 11 |

ISBN (Print) | 9783030027377 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 11th International Conference on Internet and Distributed Computing Systems, IDCS 2018 - Tokyo, Japan Duration: 2018 Oct 11 → 2018 Oct 13 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11226 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th International Conference on Internet and Distributed Computing Systems, IDCS 2018 |
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Country | Japan |

City | Tokyo |

Period | 18/10/11 → 18/10/13 |

### Fingerprint

### Keywords

- Combinations
- Complexity
- Optimization
- Parallel computing
- Representation
- Unranking

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Internet and Distributed Computing Systems - 11th International Conference, IDCS 2018, Proceedings*(pp. 16-26). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11226 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-02738-4_2

**Towards the Succinct Representation of m Out of n.** / Parque Tenorio, Victor; Miyashita, Tomoyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Internet and Distributed Computing Systems - 11th International Conference, IDCS 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11226 LNCS, Springer-Verlag, pp. 16-26, 11th International Conference on Internet and Distributed Computing Systems, IDCS 2018, Tokyo, Japan, 18/10/11. https://doi.org/10.1007/978-3-030-02738-4_2

}

TY - GEN

T1 - Towards the Succinct Representation of m Out of n

AU - Parque Tenorio, Victor

AU - Miyashita, Tomoyuki

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Combinations of n objects taken m at the time are ubiquitous in a wide range of combinatorial problems. In this paper, we introduce a novel approach to generate combinations from given integer numbers by using a gradient-based algorithm through plural number of CPU and GPU processors. The time complexity is bounded by O(m2) when using a single processor, and bounded by O(mlog m) when using at most O(m/ log m) processors. Relevant computational experiments confirmed the practical efficiency within computationally allowable limits. Our approach offers the building blocks to represent combinations with succinct encoding and complexity being independent of n, which is meritorious when n is very large, or when n is time-varying.

AB - Combinations of n objects taken m at the time are ubiquitous in a wide range of combinatorial problems. In this paper, we introduce a novel approach to generate combinations from given integer numbers by using a gradient-based algorithm through plural number of CPU and GPU processors. The time complexity is bounded by O(m2) when using a single processor, and bounded by O(mlog m) when using at most O(m/ log m) processors. Relevant computational experiments confirmed the practical efficiency within computationally allowable limits. Our approach offers the building blocks to represent combinations with succinct encoding and complexity being independent of n, which is meritorious when n is very large, or when n is time-varying.

KW - Combinations

KW - Complexity

KW - Optimization

KW - Parallel computing

KW - Representation

KW - Unranking

UR - http://www.scopus.com/inward/record.url?scp=85055672556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055672556&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-02738-4_2

DO - 10.1007/978-3-030-02738-4_2

M3 - Conference contribution

AN - SCOPUS:85055672556

SN - 9783030027377

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 16

EP - 26

BT - Internet and Distributed Computing Systems - 11th International Conference, IDCS 2018, Proceedings

A2 - Guerrieri, Antonio

A2 - Jung, Jason J.

A2 - Fortino, Giancarlo

A2 - Sun, Jingtao

A2 - Xiang, Yang

PB - Springer-Verlag

ER -