Random generation of words in an algebraic language in linear binary space

Goldwurm, Massimiliano

doi:10.1016/0020-0190(95)00025-8

Cited by 21 publications

(13 citation statements)

References 6 publications

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“…Ambiguous grammars are considered in [2], but in a different way. Other references on random generations of words of context-free languages are [2,10,11,13], however these works do not consider the enumeration problem. Can one enumerate with linear delay finite parts of context-free languages L, say L[n] or L (n) in lexicographic order?…”

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confidence: 99%

Linear delay enumeration and monadic second-order logic

Courcelle

2009

Discrete Applied Mathematics

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a b s t r a c tThe results of a query expressed by a monadic second-order formula on a tree, on a graph or on a relational structure of tree-width at most k, can be enumerated with a delay between two outputs proportional to the size of the next output. This is possible by using a preprocessing that takes time O(n · log(n)), where n is the number of vertices or elements.One can also output directly the i-th element with respect to a fixed ordering, however, in more than linear time in its size. These results extend to graphs of bounded clique-width. We also consider the enumeration of finite parts of recognizable sets of terms specified by parameters such as size, height or Strahler number.

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confidence: 99%

Linear delay enumeration and monadic second-order logic

Courcelle

2009

Discrete Applied Mathematics

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“…Then, using the recursive method of Flajolet, Zimmerman, and Van Cutsem (1994) (which can be seen as a wide generalization to combinatorial structures of what Hickey and Cohen (1983) did for context-free grammars), such paths of length n can be generated in O(n ln n) average time. Goldwurm (1995) proved that this can be done with the same time complexity, with only O(n) memory. The Boltzmann method introduced by Duchon, Flajolet, Louchard, and Schaeffer (2004) is also a way to get a linear average time random generator for paths of length within [(1 − )n, (1 + )n].…”

Section: Uniform Random Generationmentioning

confidence: 95%

Lattice paths with catastrophes

Banderier

Wallner

2017

Electronic Notes in Discrete Mathematics

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In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behaviour as classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quantifies some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continued fraction expansion. Furthermore, we prove several formulae for related combinatorial structures conjectured in the On-Line Encyclopedia of Integer Sequences. Thanks to the kernel method and via analytic combinatorics, we provide the enumeration and limit laws of these "lattice paths with catastrophes" for any finite set of jumps. We end with an algorithm to generate such lattice paths uniformly at random.

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“…Using a grammar to produce bicolored rooted ordered trees with n nodes where all the nodes of the last branch are colored white, and using Goldwurm's algorithm [17], a random outerplanar map can be generated uniformly with O(n) space and O(n 2 ) average time. Using Floating-Point Arithmetic [12], this average time complexity can be reduced to O(n 1+ǫ ).…”

Section: Introductionmentioning

confidence: 99%

Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation

Gavoille¹,

Hanusse²

2005

JGAA

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In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decomposition, constructible in linear time in the Word-RAM model, implies the existence of bijection between rooted outerplanar maps with n nodes and bicolored rooted ordered trees with n nodes where all the nodes of the last branch are colored white. As a consequence, for rooted outerplanar maps of n nodes, we derive:• an enumeration formula, and an asymptotic of 2 3n−Θ(log n) ;• an optimal data structure of asymptotically 3n bits, built in O(n) time, supporting adjacency and degree queries in worst-case constant time and neighbors query of a degree-d node in worst-case O(d) time.• an O(n) expected time uniform random generating algorithm.

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Random generation of words in an algebraic language in linear binary space

Cited by 21 publications

References 6 publications

Linear delay enumeration and monadic second-order logic

Linear delay enumeration and monadic second-order logic

Lattice paths with catastrophes

Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation

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