Mathematics and Computer Science II

n-Colored Maps and Multilabel n-Colored Trees.- Limit Laws for Basic Parameters of Lattice Paths with Unbounded Jumps.- Counting Walks in the Quarter Plane.- Bijective Construction of Equivalent Eco-systems.- Random Boundary of a Planar Map.- Enumération des 2-arbres k-gonaux.- Breadth First Search, Triangle-Free Graphs and Brownian Motion.- Random Planar Lattices and Integrated SuperBrownian Excursion.- The Diameter of a Long-Range Percolation Graph.- Giant Components for Two Expanding Graph Processes.- Coloring Random Graphs - an Algorithmic Perspective.- A Sharp Threshold for a Non-monotone Digraph Property.- Approximability of Paths Coloring Problem in Mesh and Torus Networks.- Minimal Spanning Trees for Graphs with Random Edge Lengths.- Generalized Pattern Matching Statistics.- A Note on Random Suffix Search Trees.- On the Profile of Random Forests.- On the Number of Heaps and the Cost of Heap Construction.- A Combinatorial Problem Arising in Information Theory: Precise Minimax Redundancy for Markov Sources.- Analysis of Quickfind with Small Subfiles.- Distribution of the Size of Simplified or Reduced Trees.- Digits and Beyond.- Growth Rate and Ergodicity Conditions for a Class of Random Trees.- Ideals in a Forest, One-Way Infinite Binary Trees and the Contraction Method.- On Random Walks in Random Environment on Trees and Their Relationship with Multiplicative Chaos.- Note on Exact and Asymptotic Distributions of the Parameters of the Loop-Erased Random Walk on the Complete Graph.- Convergence Rate for Stable Weighted Branching Processes.- Reduced Branching Processes in Random Environment.- A Cooperative Approach to Rényi's Parking Problem on the Circle.- On the Noise Sensitivity of Monotone Functions.- Apprentissage de Séquences Non-Indépendantesd'Exemples.- Entropy Reduction Strategies on Tree Structured Retrieval Spaces.- Zero-One Law Characterizations of ?0.- Further Applications of Chebyshev Polynomials in the Derivation of Spanning Tree Formulas for Circulant Graphs.- Key words.- List of Authors.

Zusammenfassung

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.