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 | |
| 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
Efficient enumeration of all ladder lotteries and its application. / Yamanaka, Katsuhisa; Nakano, Shin ichi; Matsui, Yasuko; Uehara, Ryuhei; Nakada, Kento.
In: Theoretical Computer Science, Vol. 411, No. 16-18, 28.03.2010, p. 1714-1722.Research output: Contribution to journal › Article
}
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 -