Results 1  10
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155
A Gray code for fixeddensity necklaces and Lyndon words in constant amortized time
 Theoretical Computer Science
"... This paper develops a constant amortized time algorithm to produce the cyclic coollex Gray code for fixeddensity binary necklaces, Lyndon words, and pseudonecklaces. It is the first Gray code for these objects that achieves this time bound. The algorithm is applied: (i) to develop a constant amor ..."
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Cited by 4 (3 self)
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This paper develops a constant amortized time algorithm to produce the cyclic coollex Gray code for fixeddensity binary necklaces, Lyndon words, and pseudonecklaces. It is the first Gray code for these objects that achieves this time bound. The algorithm is applied: (i) to develop a constant
FIXEDDENSITY DE BRUIJN SEQUENCES ∗
"... Abstract. De Bruijn sequences are circular strings of length 2 n whose substrings are the binary strings of length n. Our focus is on de Bruijn sequences for binary strings that have the same density (number of 1s). We construct circular strings of length ( n−1) ( n−1) + whose substrings of length ..."
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Cited by 1 (1 self)
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n −1 are the binary strings with density d or d −1. We call these fixeddensity d d−1 de Bruijn sequences since they have length ( n) and each substring uniquely extends to a binary string of length n with density d d by appending its ‘missing ’ redundant bit. Our construction is reminiscent
Generating Bracelets in Constant Amortized Time
 SIAM JOURNAL ON COMPUTING
, 2001
"... A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e., listing) kary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal in the s ..."
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Cited by 11 (3 self)
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in the sense that the running time is proportional to the number of bracelets produced. This is an improvement by a factor of n (where n is the length of the bracelets being generated) over the fastest, previously known algorithm to generate bracelets.
Generating Bracelets in Constant Amortized Time
, 2001
"... Abstract A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (ie., listing) kary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal ..."
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in the sense that the running time is proportional to the number of bracelets produced. This is an improvement by a factor of n (where n is the length of the bracelets being generated) over the fastest, previously known algorithm to generate bracelets.
Shift Gray Codes
, 2009
"... Combinatorial objects can be represented by strings, such as 21534 for the permutation (1 2) (3 5 4), or 110100 for the binary tree corresponding to the balanced parentheses (()()). Given a string s = s1s2⋯sn, the rightshift operation ��→ shift(s, i, j) replaces the substring sisi+1⋯sj by si+1⋯sjsi ..."
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Cited by 7 (4 self)
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⋯sjsi. In other words, si is rightshifted into position j by applying the permutation (j j −1 ⋯ i) to the indices of s. Rightshifts include prefixshifts (i = 1) and adjacenttranspositions (j = i + 1). A fixedcontent language is a set of strings that contain the same multiset of symbols. Given a
Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
, 2000
"... this paper ## Sawada 23 developed an algorithm to generate kary bracelets in constant ## amortized time. Proskurowski et al. 17 show that the orbits of the ' Z. Z. Z . composition of b and d can be generated in amortized Oktime, which is CAT if k is fixed. It remains an interesting challenge ..."
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Cited by 22 (8 self)
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this paper ## Sawada 23 developed an algorithm to generate kary bracelets in constant ## amortized time. Proskurowski et al. 17 show that the orbits of the ' Z. Z. Z . composition of b and d can be generated in amortized Oktime, which is CAT if k is fixed. It remains an interesting challenge
Generating Necklaces and Strings with Forbidden Substrings
 in Computing and Combinatorics, Lecture Notes in Comput. Sci. 1858
"... Given a length m string f over a kary alphabet and a positive integer n, we develop efficient algorithms to generate (a) all kary strings of length n that have no substring equal to f , (b) all kary circular strings of length n that have no substring equal to f , and (c) all kary necklaces ..."
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Cited by 9 (2 self)
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Given a length m string f over a kary alphabet and a positive integer n, we develop efficient algorithms to generate (a) all kary strings of length n that have no substring equal to f , (b) all kary circular strings of length n that have no substring equal to f , and (c) all kary necklaces
Generating Unlabeled Necklaces and Irreducible Polynomials over GF(2)
, 1998
"... Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A kary necklace is an equivalence class of kary strings under rotation (the cyclic group). A kary unlabeled necklace is an equivalence class of kary strings under ro ..."
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Cited by 1 (1 self)
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rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algorithms for generating (i.e., listing) all necklaces and binary unlabeled necklaces. Generalization is made to the case where no substring 0 t occurs, for fixed t. All these algorithms have optimal running times
BINARY BUBBLE LANGUAGES AND COOLLEX ORDER
"... A bubble language is a set of binary strings with a simple closure property: The first 01 of any string can be replaced by 10 to obtain another string in the set. Natural representations of many combinatorial objects are bubble languages. Examples include binary string representations of kary trees ..."
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Cited by 6 (4 self)
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ary trees, unit interval graphs, linearextensions of Bposets, binary necklaces and Lyndon words, and feasible solutions to knapsack problems. In colexicographic order, fixeddensity binary strings are ordered so that their suffixes of the form 10i occur (recursively) in the order i = max,max −1,...,min
Results 1  10
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155