Ebook: Probabilistic methods for algorithmic discrete mathematics

The book gives an accessible account of modern probabilistic methodsfor analyzing combinatorial structures and algorithms. It will be anuseful guide for graduate students and researchers. Special featuresincluded: a simple treatment of Talagrand's inequalities and theirapplications; an overview and many carefully worked out examples ofthe probabilistic analysis of combinatorial algorithms; a discussionof the "exact simulation" algorithm (in the context of Markov ChainMonte Carlo Methods); a general method for finding asymptoticallyoptimal or near optimal graph colouring, showing how theprobabilistic method may be fine-tuned to exploit the structure ofthe underlying graph; a succinct treatment of randomized algorithmsand derandomization techniques.