Efficient enumeration of all ladder lotteries and its application

Katsuhisa Yamanaka; Shin ichi Nakano; Yasuko Matsui; Ryuhei Uehara; Kento Nakada

doi:10.1016/j.tcs.2010.01.002

Efficient enumeration of all ladder lotteries and its application

Katsuhisa Yamanaka, Shin ichi Nakano, Yasuko Matsui, Ryuhei Uehara, Kento Nakada

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	1714-1722
Number of pages	9
Journal	Theoretical Computer Science
Volume	411
Issue number	16-18
DOIs	https://doi.org/10.1016/j.tcs.2010.01.002
Publication status	Published - Mar 28 2010
Externally published	Yes

Keywords

Enumeration algorithm
Family tree
Ladder lottery
Pseudoline arrangement

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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title = "Efficient enumeration of all ladder lotteries and its application",

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 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.",

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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.

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KW - Ladder lottery

KW - Pseudoline arrangement

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Efficient enumeration of all ladder lotteries and its application

Abstract

Keywords

ASJC Scopus subject areas

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