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The Art of Computer Programming: Volume IV: Fascicle 2: Generating All Tuples and Permutations
The Art of Computer Programming: Volume IV: Fascicle 2: Generating All Tuples and Permutations,Donald E. Knuth
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The Art of Computer Programming: Volume IV: Fascicle 2: Generating All Tuples and Permutations
(
Citations: 37
)
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Donald E. Knuth
Published in 2005.
Cumulative
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Citation Context
(16)
...An introduction to the topic is given by Knuth [
5
], which opposed to the original text does not demand a background in group theory...
Florian Wisser
.
Creating Possible Worlds Using Sims Tables for the Imperfect Informati...
...Section 7.2.1 of Knuth’s The Art of Computer Programming [
10
,11,12] is an exceptional reference...
...Therefore, r240 =5a ndt240 = 2. For a more complete example, the staircase strings of length 3 appear in column (a) of Table 1 in colex order, while columns (b) and (c) contain R4 and T4. (Table 1 appears on page 371 and columns (b) and (c) have been offset by half a row to emphasize the transition between successive staircase strings.) To generate R and T , one can simply augment Algorithm M (Mixedradix generation) in 7.2.1.1 of [
10
] ...
...To generate R and T by a loopless algorithm, we can again follow [
10
]...
...Algorithm H in [
10
] generates multiradix strings in reflected Gray code order...
...As Knuth points out at the beginning of Section 7.2.1.2 in The Art of Computer Programming [
10
], an iterative algorithm for creating the permutations of � n� in colex order dates back to the 14thcentury...
...Which other orders of permutations can be explained by the specialization of Algorithm H [
10
] to staircase strings or downward staircase strings (using bases n, n − 1 ,..., 2)? O(1)Time Unsorting in a Boustrophedon Linked List 379...
Aaron Williams
.
O(1)Time Unsorting by PrefixReversals in a Boustrophedon Linked List
...The area is so important to computer science that Knuth has dedicated over 400 pages to the subject in his upcoming volume of The Art of Computer Programming [27,
28
]...
...The reader is directed towards [
28
, 27, 29] and [31] for excellent treatments of the subject...
Aaron Williams
.
Loopless generation of multiset permutations using a constant number o...
...5 A canonical coordinate sequence is the one in which each coordinate k appears before the first appearance of k + 1 [
11
]...
Yury Chebiryak
,
et al.
Finding Lean Induced Cycles in Binary Hypercubes
...a Gray code [
15
] when enumerating steps, always using one group operation per step (this is especially useful for small p, saving up to a factor of 2). A more significant optimization available with Shanks’ method is the ability to perform k discrete logarithms in a group of size N using 2 √ kN (rather than 2k √ N) group operations by storing √ kN baby steps in a lookup table and then taking p N/k...
Andrew V. Sutherland
.
Structure computation and discrete logarithms in finite abelian pgrou...
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Citations
(37)
Faster Generation of Shorthand Universal Cycles for Permutations
(
Citations: 1
)
Alexander E. Holroyd
,
Frank Ruskey
,
Aaron Williams
Conference:
Computing and Combinatorics  COCOON
, pp. 298307, 2010
Creating Possible Worlds Using Sims Tables for the Imperfect Information Card Game Schnapsen
Florian Wisser
Conference:
International Conference on Tools with Artificial Intelligence  ICTAI
, vol. 2, pp. 710, 2010
O(1)Time Unsorting by PrefixReversals in a Boustrophedon Linked List
Aaron Williams
Conference:
Fun with Algorithms  FUN
, pp. 368379, 2010
Long paths in hypercubes with a quadratic number of faults
(
Citations: 9
)
Tomás Dvorák
,
Václav Koubek
Journal:
Information Sciences  ISCI
, vol. 179, no. 21, pp. 37633771, 2009
Loopless generation of multiset permutations using a constant number of variables by prefix shifts
(
Citations: 4
)
Aaron Williams
Conference:
ACMSIAM Symposium on Discrete Algorithms  SODA
, pp. 987996, 2009