### Abstract

A ladder lottery, known as "Amidakuji" in Japan, is a common way to choose a permutation randomly. A ladder lottery L corresponding to a given permutation π is optimal if L has the minimum number of horizontal lines among the ladder lotteries corresponding to π. In this paper we show that for any two optimal ladder lotteries L_{1} and L_{2} of a permutation, there exists a sequence of local modifications which transforms L_{1} into L_{2}. We also give an algorithm to enumerate all optimal ladder lotteries of a given permutation. By setting π = (n, n - 1, ..., 1), the algorithm enumerates all arrangements of n pseudolines efficiently. By implementing the algorithm we compute the number of arrangements of n pseudolines for each n ≤ 11.

Original language | English |
---|---|

Pages (from-to) | 1714-1722 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 411 |

Issue number | 16-18 |

DOIs | |

Publication status | Published - Mar 28 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Enumeration algorithm
- Family tree
- Ladder lottery
- Pseudoline arrangement

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*411*(16-18), 1714-1722. https://doi.org/10.1016/j.tcs.2010.01.002

**Efficient enumeration of all ladder lotteries and its application.** / Yamanaka, Katsuhisa; Nakano, Shin ichi; Matsui, Yasuko; Uehara, Ryuhei; Nakada, Kento.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 411, no. 16-18, pp. 1714-1722. https://doi.org/10.1016/j.tcs.2010.01.002

}

TY - JOUR

T1 - Efficient enumeration of all ladder lotteries and its application

AU - Yamanaka, Katsuhisa

AU - Nakano, Shin ichi

AU - Matsui, Yasuko

AU - Uehara, Ryuhei

AU - Nakada, Kento

PY - 2010/3/28

Y1 - 2010/3/28

N2 - A ladder lottery, known as "Amidakuji" in Japan, is a common way to choose a permutation randomly. A ladder lottery L corresponding to a given permutation π is optimal if L has the minimum number of horizontal lines among the ladder lotteries corresponding to π. In this paper we show that for any two optimal ladder lotteries L1 and L2 of a permutation, there exists a sequence of local modifications which transforms L1 into L2. We also give an algorithm to enumerate all optimal ladder lotteries of a given permutation. By setting π = (n, n - 1, ..., 1), the algorithm enumerates all arrangements of n pseudolines efficiently. By implementing the algorithm we compute the number of arrangements of n pseudolines for each n ≤ 11.

AB - A ladder lottery, known as "Amidakuji" in Japan, is a common way to choose a permutation randomly. A ladder lottery L corresponding to a given permutation π is optimal if L has the minimum number of horizontal lines among the ladder lotteries corresponding to π. In this paper we show that for any two optimal ladder lotteries L1 and L2 of a permutation, there exists a sequence of local modifications which transforms L1 into L2. We also give an algorithm to enumerate all optimal ladder lotteries of a given permutation. By setting π = (n, n - 1, ..., 1), the algorithm enumerates all arrangements of n pseudolines efficiently. By implementing the algorithm we compute the number of arrangements of n pseudolines for each n ≤ 11.

KW - Enumeration algorithm

KW - Family tree

KW - Ladder lottery

KW - Pseudoline arrangement

UR - http://www.scopus.com/inward/record.url?scp=77949272092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949272092&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2010.01.002

DO - 10.1016/j.tcs.2010.01.002

M3 - Article

AN - SCOPUS:77949272092

VL - 411

SP - 1714

EP - 1722

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 16-18

ER -