Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff-Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff-Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff-Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff-Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

The volume contains the papers selected for presentation at IPCO 2008, the 13th International Conference on Integer Programming and Combinatorial - timization that was held in Bertinoro (Italy), May 26-28, 2008. The IPCO series of conferences, sponsored by the Mathematical Progr- ming Society, highlights recent developments in theory, computation, and app- cation of integer programming and combinatorial optimization. The ?rst conf- ence took place in 1990; starting from IPCO 1995, the proceedings are published in the Lecture Notes in Computer Science series. The 12 previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995 [LNCS 920], Vancouver (Canada) 1996 [LNCS 1084], Houston (USA) 1998 [LNCS 1412], Graz (Austria) 1999 [LNCS 1610], Utrecht (The Netherlands) 2001 [LNCS 2081], Boston (USA) 2002 [LNCS 2337], New York (USA) 2004 [LNCS 2986], Berlin (Germany) 2005 [LNCS 3509], and Ithaca (USA) 2007 [LNCS 4168]. The c- ference is not held in the years when the International Symposium of the Ma- ematical Programming Society takes place.