### Abstract

We consider a variant of the metrical task system (MTS) problem under the uniform metric, where each decision corresponds to some combinatorial object in a fixed set (e.g., the set of all s-t paths of a fixed graph). Typical algorithms such as Marking algorithm are not known to solve this problem efficiently and straightforward implementations takes exponential time for many classes of combinatorial sets. We propose a modification of Marking algorithm, which we call Weighted Marking algorithm. We show that Weighted Marking algorithm still keeps O(log n) competitive ratio for the standard MTS problem with n states. On the other hand, combining with known sampling techniques for combinatorial sets, Weighted Marking algorithm works efficiently for various classes of combinatorial sets.

Original language | English |
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Title of host publication | Algorithmic Learning Theory - 27th International Conference, ALT 2016, Proceedings |

Publisher | Springer Verlag |

Pages | 276-287 |

Number of pages | 12 |

Volume | 9925 LNAI |

ISBN (Print) | 9783319463780 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 27th International Conference on Algorithmic Learning Theory, ALT 2016 - Bari, Italy Duration: Oct 19 2016 → Oct 21 2016 |

### 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 | 9925 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 27th International Conference on Algorithmic Learning Theory, ALT 2016 |
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Country | Italy |

City | Bari |

Period | 10/19/16 → 10/21/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithmic Learning Theory - 27th International Conference, ALT 2016, Proceedings*(Vol. 9925 LNAI, pp. 276-287). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9925 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-319-46379-7_19

**A combinatorial metrical task system problem under the uniform metric.** / Nakazono, Takumi; Moridomi, Ken Ichiro; hatano, kohei; Takimoto, Eiji.

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

*Algorithmic Learning Theory - 27th International Conference, ALT 2016, Proceedings.*vol. 9925 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9925 LNAI, Springer Verlag, pp. 276-287, 27th International Conference on Algorithmic Learning Theory, ALT 2016, Bari, Italy, 10/19/16. https://doi.org/10.1007/978-3-319-46379-7_19

}

TY - GEN

T1 - A combinatorial metrical task system problem under the uniform metric

AU - Nakazono, Takumi

AU - Moridomi, Ken Ichiro

AU - hatano, kohei

AU - Takimoto, Eiji

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We consider a variant of the metrical task system (MTS) problem under the uniform metric, where each decision corresponds to some combinatorial object in a fixed set (e.g., the set of all s-t paths of a fixed graph). Typical algorithms such as Marking algorithm are not known to solve this problem efficiently and straightforward implementations takes exponential time for many classes of combinatorial sets. We propose a modification of Marking algorithm, which we call Weighted Marking algorithm. We show that Weighted Marking algorithm still keeps O(log n) competitive ratio for the standard MTS problem with n states. On the other hand, combining with known sampling techniques for combinatorial sets, Weighted Marking algorithm works efficiently for various classes of combinatorial sets.

AB - We consider a variant of the metrical task system (MTS) problem under the uniform metric, where each decision corresponds to some combinatorial object in a fixed set (e.g., the set of all s-t paths of a fixed graph). Typical algorithms such as Marking algorithm are not known to solve this problem efficiently and straightforward implementations takes exponential time for many classes of combinatorial sets. We propose a modification of Marking algorithm, which we call Weighted Marking algorithm. We show that Weighted Marking algorithm still keeps O(log n) competitive ratio for the standard MTS problem with n states. On the other hand, combining with known sampling techniques for combinatorial sets, Weighted Marking algorithm works efficiently for various classes of combinatorial sets.

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U2 - 10.1007/978-3-319-46379-7_19

DO - 10.1007/978-3-319-46379-7_19

M3 - Conference contribution

AN - SCOPUS:84994116122

SN - 9783319463780

VL - 9925 LNAI

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

SP - 276

EP - 287

BT - Algorithmic Learning Theory - 27th International Conference, ALT 2016, Proceedings

PB - Springer Verlag

ER -