P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....an object grammar. It is most often described with drawings. For instance, the standard decomposition of complete binary trees is an object grammar (Figure 1) The formalism given here for object grammars [9] generalizes the one for context free grammars. It is akin to the work of Flajolet al... [12] allowing for the specication of structures by grammars involving set, sequence and cycle constructions. One can also categorize object grammars as belonging to the domain of Universal Algebra and Magmas [11, 15] Finally, our approach is related to the Theory of Species [2, 13] which gives a ....

P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.

....object grammar. It is most often described with drawings. For instance, the standard decomposition of complete binary trees is an object grammar (Figure 1) The formalism given here for object grammars [7, 8] generalizes the one for context free grammars. It is akin to the work of Flajolet al... [10, 11] allowing for the specication of structures by grammars involving set, sequence and cycle constructions. One can also categorize object grammars as belonging to the domain of Universal Algebra and Magmas [9, 15, 1] Finally, our approach is related to the Theory of Species [3, 14] which gives a ....

.... and Wilf [16] then by Hickey and Cohen in the case of context free languages [13] and by Greene within the framework of the labelled formal languages [12] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method concerning their specications of structures [11]. The methods that they have examined enable to start from any hight level specication of decomposable class and compile automatically procedures that solve the corresponding random generation problem. They have presented two closely related groups of methods : the sequentiel algorithms (linear ....

[Article contains additional citation context not shown here]

P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.

.... case of context free languages [10] and by Greene within the framework of the labelled formal languages [9] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method with specifications of structures by grammars involving set, sequence and cycle constructions [8]. The methods that they have examined enable to start from any hight level specification of decomposable class and compile automatically procedures that solve the corresponding random generation problem. They have presented two closely related groups of methods: the sequential algorithms (linear ....

.... complexity O(kl(k l) when applied to objects of valuation x k q l , assuming the enumeration tables have been computed once for all in O(k 2 l 2 ) time (see [6] for the general case of valuation) If one only considers an algebraic parameter (x k ) the complexity is the same as in [8], and the boustrophedonic search can be used. Note that, as in [8] the complexity is related to the number of arithmetic operations, unit cost is taken for the manipulation of a large integer. The path taken here is eminently praticable and the method has been implemented in the Maple language ....

[Article contains additional citation context not shown here]

Flajolet, P., Zimmermann, P. and Van Cutsem, B. (1994). A Calculus for the Random Generation of Combinatorial Structures. Theoretical Computer Science 132: 1--35.

....trees. context free languages [10] and by Greene within the framework of the labelled formal languages [9] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method with specications of structures by grammars involving set, sequence and cycle constructions [8]. The methods that they have examined enable to start from any hight level specication of decomposable class and compile automatically procedures that solve the corresponding random generation problem. They have presented two closely related groups of methods : the sequential algorithms (linear ....

.... complexity O(kl(k l) when applied to objects of valuation x k q l , assuming the enumeration tables have been computed once for all in O(k 2 l 2 ) time (see [6] for the general case of valuation) If one only considers an algebraic parameter (x k ) the complexity is the same as in [8] and the boustrophedonic search can be used. The path taken here is eminently praticable and the method has been implemented in the Maple language (package named qAlGO) Section 5 gives some results obtained with this program concerning the uniform random generation of convex polyominoes ....

[Article contains additional citation context not shown here]

P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.

....an object grammar. It is most often described with drawings. For instance, the standard decomposition of complete binary trees is an object grammar (Figure 1) The formalism given here for object grammars [9] generalizes the one for context free grammars. It is akin to the work of Flajolet al... [12] allowing for the speci cation of structures by grammars involving set, sequence and cycle constructions. One can also categorize object grammars as belonging to the domain of Universal Algebra and Magmas [11, 15] Finally, our approach is related to the Theory of Species [2, 13] which gives a ....

P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.

....object grammar. It is most often described with drawings. For instance, the standard decomposition of complete binary trees is an object grammar (Figure 1) The formalism given here for object grammars [7, 8] generalizes the one for context free grammars. It is akin to the work of Flajolet al... [10, 11] allowing for the speci cation of structures by grammars involving set, sequence and cycle constructions. One can also categorize object grammars as belonging to the domain of Universal Algebra and Magmas [9, 15, 1] Finally, our approach is related to the Theory of Species [3, 14] which gives a ....

.... and Wilf [16] then by Hickey and Cohen in the case of context free languages [13] and by Greene within the framework of the labelled formal languages [12] Recently, Flajolet, Zimmermann and Van Cutsem have given a systematic approach for this method concerning their speci cations of structures [11]. The methods that they have examined enable to start from any hight level speci cation of decomposable class and compile automatically procedures that solve the corresponding random generation problem. They have presented two closely related groups of methods : the sequentiel algorithms (linear ....

[Article contains additional citation context not shown here]

P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for the random generation of combinatorial structures. Theoretical Computer Science, 132:135, 1994.

....package for the random generation of combinatorial structures Paul Zimmermann 1 Gaia is a computer algebra package that helps counting and drawing random combinatorial structures of various sorts. It is an implementation of the calculus developed by Ph. Flajolet, B. Van Cutsem and the author in [5]. Given a combinatorial specification and an integer n, it draws a random object uniformly amongst all size n structures. It applies to all decomposable structures, either labelled or unlabelled, including trees of various kinds, surjections, set partitions, permutations, functional graphs of ....

....the counting sequences up to size n. This article explains how to define a class of decomposable combinatorial structures with Gaia, how to count the number of structures of a given size, how to generate a random structure and how to use it. Details about the algorithms used will be found in [5] and [6] A simple example Once you have properly installed Gaia as a Maple package (see the section Installing the package below) it is very easy to generate a random object, for example a random binary tree: maple with(gaia) binarytree : B = Union(Z, Prod(B,B) ....

[Article contains additional citation context not shown here]

Flajolet, P., Zimmermann, P., and Cutsem, B. V. A calculus for the random generation of combinatorial structures. Theoretical Comput. Sci.. 29 pages. To appear. Also available as Inria Research Report number 1830.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC