The Experts below are selected from a list of 5487 Experts worldwide ranked by ideXlab platform
Thom Fruhwirth - One of the best experts on this subject based on the ideXlab platform.
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CSCLP - Complete propagation rules for Lexicographic Order constraints over arbitrary domains
Lecture Notes in Computer Science, 2006Co-Authors: Thom FruhwirthAbstract:We give an efficiently executable specification of the global constraint of Lexicographic Order in the Constraint Handling Rules (CHR) language. In contrast to previous approaches, the implementation is short and concise without giving up on the best known worst case time complexity. It is incremental and concurrent by nature of CHR. It is provably correct and confluent. It is independent of the underlying constraint system, and therefore not restricted to finite domains. We have found a direct recursive decomposition of the problem. We also show completeness of constraint propagation, i.e. that all possible logical consequences of the constraint are generated by the implementation. Finally, we report about some practical implementation experiments.
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complete propagation rules for Lexicographic Order constraints over arbitrary domains
Lecture Notes in Computer Science, 2005Co-Authors: Thom FruhwirthAbstract:We give an efficiently executable specification of the global constraint of Lexicographic Order in the Constraint Handling Rules (CHR) language. In contrast to previous approaches, the implementation is short and concise without giving up on the best known worst case time complexity. It is incremental and concurrent by nature of CHR. It is provably correct and confluent. It is independent of the underlying constraint system, and therefore not restricted to finite domains. We have found a direct recursive decomposition of the problem. We also show completeness of constraint propagation, i.e. that all possible logical consequences of the constraint are generated by the implementation. Finally, we report about some practical implementation experiments.
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logical rules for a Lexicographic Order constraint solver
Proceedings of CHR 2005 Second Workshop on Constraint Handling Rules, 2005Co-Authors: Thom FruhwirthAbstract:We give an executable specification of the global constraint of Lexicographic Order in Constraint Handling Rules (CHR) language. In contrast to previous approaches, the implementation is short and concise without giving up on linear time worst case time complexity. It is incremental and concurrent by nature of CHR. It is provably correct and confluent. It is independent of the underlying constraint system, and therefore not restricted to finite domains. We also show completeness of constraint propagation, i.e. that all possible consequences of the constraint are generated by the implementation. Our algorithm is encoded by three pairs of rules, two corresponding to base cases, two performing the obvious traversal of the sequences to be compared and two covering a not so obvious special case when the Lexicographic constraint has a unique solution.
Shunchieh Chang - One of the best experts on this subject based on the ideXlab platform.
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Amortized efficiency of generation, ranking and unranking left-child sequences in Lexicographic Order
Discrete Applied Mathematics, 2019Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:Abstract A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. (2014) for representing binary trees. They pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on this characterization, there is an easily implementing algorithm that uses generate-and-test approach to filter all LC-sequences of binary trees with n internal nodes in Lexicographic Order, while in general it is not efficient at all. In this paper, we first design two novel rotations that allow us to drastically alter the shape of binary trees (and thus their corresponding LC-sequences). As an application, these operations can be employed to generate all LC-sequences in Lexicographic Order. Accordingly, we present a more efficient algorithm associated with the new types of rotations for generating all LC-sequences and show that it takes only constant amortized running cost. Moreover, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen (1987) to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With the help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of O ( n ) time and space.
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amortized efficiency of ranking and unranking left child sequences in Lexicographic Order
Conference on Combinatorial Optimization and Applications, 2016Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. [19] for representing binary trees. In particular, they pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on such a characterization, there is an algorithm to generate all LC-sequences of binary trees with n internal nodes in Lexicographic Order. In this paper, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen [8] to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With a help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of \(\mathcal {O}(n)\) time and space.
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COCOA - Amortized Efficiency of Ranking and Unranking Left-Child Sequences in Lexicographic Order
Combinatorial Optimization and Applications, 2016Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. [19] for representing binary trees. In particular, they pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on such a characterization, there is an algorithm to generate all LC-sequences of binary trees with n internal nodes in Lexicographic Order. In this paper, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen [8] to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With a help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of \(\mathcal {O}(n)\) time and space.
Thomas Noll - One of the best experts on this subject based on the ideXlab platform.
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matching Lexicographic and conjugation Orders on the conjugation class of a special sturmian morphism
International Conference on Combinatorics on Words, 2017Co-Authors: David Clampitt, Thomas NollAbstract:The conjugation class of a special Sturmian morphism carries a natural linear Order by virtue of the two elementary conjugations \(conj_a\) and \(conj_b\) with the single letters a and b, with the standard morphism of the class as the smallest element in this Order. We show that a Lexicographic Order on the morphisms of the given conjugation class can be defined that matches the conjugation Order.
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WORDS - Matching Lexicographic and Conjugation Orders on the Conjugation Class of a Special Sturmian Morphism
Lecture Notes in Computer Science, 2017Co-Authors: David Clampitt, Thomas NollAbstract:The conjugation class of a special Sturmian morphism carries a natural linear Order by virtue of the two elementary conjugations \(conj_a\) and \(conj_b\) with the single letters a and b, with the standard morphism of the class as the smallest element in this Order. We show that a Lexicographic Order on the morphisms of the given conjugation class can be defined that matches the conjugation Order.
Kungjui Pai - One of the best experts on this subject based on the ideXlab platform.
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Amortized efficiency of generation, ranking and unranking left-child sequences in Lexicographic Order
Discrete Applied Mathematics, 2019Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:Abstract A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. (2014) for representing binary trees. They pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on this characterization, there is an easily implementing algorithm that uses generate-and-test approach to filter all LC-sequences of binary trees with n internal nodes in Lexicographic Order, while in general it is not efficient at all. In this paper, we first design two novel rotations that allow us to drastically alter the shape of binary trees (and thus their corresponding LC-sequences). As an application, these operations can be employed to generate all LC-sequences in Lexicographic Order. Accordingly, we present a more efficient algorithm associated with the new types of rotations for generating all LC-sequences and show that it takes only constant amortized running cost. Moreover, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen (1987) to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With the help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of O ( n ) time and space.
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a constant amortized time algorithm for generating left child sequences in Lexicographic Order
International Workshop on Frontiers in Algorithmics, 2017Co-Authors: Kungjui Pai, Jouming ChangAbstract:Wu et al. (Theoret. Comput. Sci. 556:25–33, 2014) recently introduced a new type of sequences, called left-child sequences (LC-sequences for short), for representing binary trees. They pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on this characterization, Pai et al. (International conference on combinatorial optimization and applications. Springer, Cham, pp. 505–518, 2016) showed that there is an easily implementing algorithm that uses generate-and-test approach to filter all LC-sequences of binary trees with n internal nodes in Lexicographic Order, while in general this algorithm is not efficient at all. In this paper, we design two novel rotations that allow us to drastically alter the shape of binary trees (and thus their corresponding LC-sequences). As an application, these operations can be employed to generate all LC-sequences in Lexicographic Order. Accordingly, we present a more efficient algorithm associated with the new types of rotations for generating all LC-sequences and show that it takes only constant amortized running cost.
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FAW - A Constant Amortized Time Algorithm for Generating Left-Child Sequences in Lexicographic Order
Frontiers in Algorithmics, 2017Co-Authors: Kungjui Pai, Jouming ChangAbstract:Wu et al. (Theoret. Comput. Sci. 556:25–33, 2014) recently introduced a new type of sequences, called left-child sequences (LC-sequences for short), for representing binary trees. They pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on this characterization, Pai et al. (International conference on combinatorial optimization and applications. Springer, Cham, pp. 505–518, 2016) showed that there is an easily implementing algorithm that uses generate-and-test approach to filter all LC-sequences of binary trees with n internal nodes in Lexicographic Order, while in general this algorithm is not efficient at all. In this paper, we design two novel rotations that allow us to drastically alter the shape of binary trees (and thus their corresponding LC-sequences). As an application, these operations can be employed to generate all LC-sequences in Lexicographic Order. Accordingly, we present a more efficient algorithm associated with the new types of rotations for generating all LC-sequences and show that it takes only constant amortized running cost.
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amortized efficiency of ranking and unranking left child sequences in Lexicographic Order
Conference on Combinatorial Optimization and Applications, 2016Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. [19] for representing binary trees. In particular, they pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on such a characterization, there is an algorithm to generate all LC-sequences of binary trees with n internal nodes in Lexicographic Order. In this paper, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen [8] to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With a help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of \(\mathcal {O}(n)\) time and space.
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COCOA - Amortized Efficiency of Ranking and Unranking Left-Child Sequences in Lexicographic Order
Combinatorial Optimization and Applications, 2016Co-Authors: Kungjui Pai, Jouming Chang, Shunchieh ChangAbstract:A new type of sequences called left-child sequences (LC-sequences for short) was recently introduced by Wu et al. [19] for representing binary trees. In particular, they pointed out that such sequences have a natural interpretation from the view point of data structure and gave a characterization of them. Based on such a characterization, there is an algorithm to generate all LC-sequences of binary trees with n internal nodes in Lexicographic Order. In this paper, we extend our study to the ranking and unranking problems. By integrating a measure called “left distances” introduced by Makinen [8] to represent binary trees, we develop efficient ranking and unranking algorithms for LC-sequences in Lexicographic Order. With a help of aggregate analysis, we show that both ranking and unranking algorithms can be run in amortized cost of \(\mathcal {O}(n)\) time and space.
David Clampitt - One of the best experts on this subject based on the ideXlab platform.
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matching Lexicographic and conjugation Orders on the conjugation class of a special sturmian morphism
International Conference on Combinatorics on Words, 2017Co-Authors: David Clampitt, Thomas NollAbstract:The conjugation class of a special Sturmian morphism carries a natural linear Order by virtue of the two elementary conjugations \(conj_a\) and \(conj_b\) with the single letters a and b, with the standard morphism of the class as the smallest element in this Order. We show that a Lexicographic Order on the morphisms of the given conjugation class can be defined that matches the conjugation Order.
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WORDS - Matching Lexicographic and Conjugation Orders on the Conjugation Class of a Special Sturmian Morphism
Lecture Notes in Computer Science, 2017Co-Authors: David Clampitt, Thomas NollAbstract:The conjugation class of a special Sturmian morphism carries a natural linear Order by virtue of the two elementary conjugations \(conj_a\) and \(conj_b\) with the single letters a and b, with the standard morphism of the class as the smallest element in this Order. We show that a Lexicographic Order on the morphisms of the given conjugation class can be defined that matches the conjugation Order.
