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112
Boltzmann Samplers For The Random Generation Of Combinatorial Structures
 Combinatorics, Probability and Computing
, 2004
"... This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combina ..."
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Cited by 67 (2 self)
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This article proposes a surprisingly simple framework for the random generation of combinatorial configurations based on what we call Boltzmann models. The idea is to perform random generation of possibly complex structured objects by placing an appropriate measure spread over the whole of a combinatorial class  an object receives a probability essentially proportional to an exponential of its size. As demonstrated here, the resulting algorithms based on realarithmetic operations often operate in linear time. They can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.
Optimal Coding and Sampling of Triangulations
, 2003
"... Abstract. We present a simple encoding of plane triangulations (aka. maximal planar graphs) by plane trees with two leaves per inner node. Our encoding is a bijection taking advantage of the minimal Schnyder tree decomposition of a plane triangulation. Coding and decoding take linear time. As a bypr ..."
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Cited by 36 (5 self)
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Abstract. We present a simple encoding of plane triangulations (aka. maximal planar graphs) by plane trees with two leaves per inner node. Our encoding is a bijection taking advantage of the minimal Schnyder tree decomposition of a plane triangulation. Coding and decoding take linear time. As a byproduct we derive: (i) a simple interpretation of the formula for the number of plane triangulations with n vertices, (ii) a linear random sampling algorithm, (iii) an explicit and simple information theory optimal encoding. 1
Uniform Random Generation of Decomposable Structures Using FloatingPoint Arithmetic
 THEORETICAL COMPUTER SCIENCE
, 1997
"... The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, ..."
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Cited by 31 (2 self)
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The recursive method formalized by Nijenhuis and Wilf [15] and systematized by Flajolet, Van Cutsem and Zimmermann [8], is extended here to floatingpoint arithmetic. The resulting ADZ method enables one to generate decomposable data structures  both labelled or unlabelled  uniformly at random, in expected O(n 1+ffl ) time and space, after a preprocessing phase of O(n 2+ffl ) time, which reduces to O(n 1+ffl ) for contextfree grammars.
Generating Labeled Planar Graphs Uniformly at Random
, 2003
"... We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that count all such graphs with n vertices and m edges, based on a decomposition into 1, 2, and 3connected components. For 3con ..."
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Cited by 25 (7 self)
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We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that count all such graphs with n vertices and m edges, based on a decomposition into 1, 2, and 3connected components. For 3connected graphs we apply a recent random generation algorithm by Schaeffer and a counting formula by Mullin and Schellenberg.
Some Probabilistic Aspects Of Set Partitions
 American Mathematical Monthly
, 1996
"... this paper, section (1.2) offers an elementary combinatorial proof of Dobinski's formula which seems simpler than other proofs in the literature (Rota [35], Berge [5], p. 44, Comtet [9], p. 211). This argument involves identities whose probabilistic interpretations are brought out later in the ..."
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Cited by 22 (2 self)
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this paper, section (1.2) offers an elementary combinatorial proof of Dobinski's formula which seems simpler than other proofs in the literature (Rota [35], Berge [5], p. 44, Comtet [9], p. 211). This argument involves identities whose probabilistic interpretations are brought out later in the paper. 1.1 Notation
A generic method for statistical testing
 In Proceedings of the 15th. IEEE International Symposium on Software Reliability Engineering (ISSRE
, 2004
"... This paper addresses the problem of selecting finite test sets and automating this selection. Among these methods, some are deterministic and some are statistical. The kind of statistical testing we consider has been inspired by the work of ThevenodFosse and Waeselynck. There, the choice of the dis ..."
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Cited by 19 (6 self)
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This paper addresses the problem of selecting finite test sets and automating this selection. Among these methods, some are deterministic and some are statistical. The kind of statistical testing we consider has been inspired by the work of ThevenodFosse and Waeselynck. There, the choice of the distribution on the input domain is guided by the structure of the program or the form of its specification. In the present paper, we describe a new generic method for performing statistical testing according to any given graphical description of the behavior of the system under test. This method can be fully automated. Its main originality is that it exploits recent results and tools in combinatorics, precisely in the area of random generation of combinatorial structures. Uniform random generation routines are used for drawing paths from the set of execution paths or traces of the system under test. Then a constraint resolution step is performed, aiming to design a set of test data that activate the generated paths. This approach applies to a number of classical coverage criteria. Moreover, we show how linear programming techniques may help to improve the quality of test, i.e. the probabilities for the elements to be covered by the test process. The paper presents the method in its generality. Then, in the last section, experimental results on applying it to structural statistical software testing are reported. 1
Generating Random Elements of Finite Distributive Lattices
 Electronic Journal of Combinatorics
, 1997
"... This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using "coupling from the past" to remove initialization bias f ..."
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Cited by 17 (1 self)
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This survey article describes a method for choosing uniformly at random from any finite set whose objects can be viewed as constituting a distributive lattice. The method is based on ideas of the author and David Wilson for using "coupling from the past" to remove initialization bias from Monte Carlo randomization.
A New Way of Automating Statistical Testing Methods
, 2001
"... We propose a new way of automating statistical structural testing, based on the combination of uniform generation of combinatorial structures, and of randomized constraint solving techniques. More precisely, we show how to draw test cases which balance the coverage of program structures according to ..."
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Cited by 16 (6 self)
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We propose a new way of automating statistical structural testing, based on the combination of uniform generation of combinatorial structures, and of randomized constraint solving techniques. More precisely, we show how to draw test cases which balance the coverage of program structures according to structural testing criteria. The control flow graph is formalized as a combinatorial structure specification. This provides a way of uniformly drawing execution paths which have suitable properties. Once a path has been drawn, the predicate characterizing those inputs which lead to its execution is solved using a constraint solving library. The constraint solver is enriched with powerful heuristics in order to deal with resolution failures and random choice strategies.