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 |
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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 |
Keywords
- Enumeration algorithm
- Family tree
- Ladder lottery
- Pseudoline arrangement
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)