## Mathematics and Computer Science II: Algorithms, Trees, Combinatorics and ProbabilitiesBrigitte Chauvin, Philippe Flajolet, Daniele Gardy, Abdelkader Mokkadem This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science. |

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### Contents

nColored Maps and Multilabel nColored Trees | 17 |

Limit Laws for Basic Parameters of Lattice Paths with Unbounded Jumps | 33 |

Counting Walks in the Quarter Plane | 49 |

Bijective Construction of Equivalent Ecosystems | 69 |

Random Boundary of a Planar Map | 83 |

Enumeration des 2arbres kgonaux | 95 |

Random Graphs and Networks | 111 |

Breadth First Search TriangleFree Graphs and Brownian Motion | 113 |

Analysis of Quickfind with Small Subfiles | 329 |

Distribution of the Size of Simplified or Reduced Trees | 332 |

Digits and Beyond | 346 |

Branching Processes and Trees | 370 |

Growth Rate and Ergodicity Conditions for a Class of Random Trees | 372 |

Ideals in a Forest OneWay Infinite Binary Trees and the Contraction Method | 384 |

On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos | 406 |

Distributions of the Parameters of the LoopErased Random Walk on the Complete Graph | 414 |

Random Planar Lattices and Integrated SuperBrownian Excursion | 127 |

The Diameter of a LongRange Percolation Graph | 147 |

Giant Components for Two Expanding Graph Processes | 161 |

Coloring Random Graphs an Algorithmic Perspective | 175 |

A Sharp Threshold for a Nonmonotone Digraph Property | 197 |

Approximability of Paths Coloring Problem in Mesh and Torus Networks | 213 |

Minimal Spanning Trees for Graphs with Random Edge Lengths | 223 |

Analysis of Algorithms and Trees | 247 |

Generalized Pattern Matching Statistics | 249 |

A Note on Random Suffix Search Trees | 267 |

On the Profile of Random Forests | 279 |

On the Number of Heaps and the Cost of Heap Construction | 295 |

Precise Minimax Redundancy for Markov Sources | 311 |

Convergence Rate for Stable Weighted Branching Processes | 432 |

Reduced Branching Processes in Random Environment | 446 |

Applied random combinatorics | 460 |

A Cooperative Approach to Renyis Parking Problem on the Circle | 462 |

On the Noise Sensitivity of Monotone Functions | 472 |

Apprentissage de Sequences NonIndependantes dExemples | 488 |

Entropy Reduction Strategies on Tree Structured Retrieval Spaces | 504 |

ZeroOne Law Characterizations of E0 | 518 |

Polynomials in the Derivation of Spanning Tree Formulas for Circulant Graphs | 532 |

Key Words | 546 |

List of Authors | 548 |