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

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

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

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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 -