Randomized algorithms

We have already seen some uses of randomization in the design of on line algorithms In these notes we shall describe other important illustrations of randomized algo rithms in other areas of the theory of algorithms For those interested in learning more about randomized algorithms we strongly recommend the forthcoming book by Motwani and Raghavan First we shall describe some basic principles which typically underly the construction of randomized algorithms The description follows a set of lectures given by R M Karp

[1]  K. N. Dollman,et al.  - 1 , 1743 .

[2]  Donald E. Knuth,et al.  The art of computer programming: sorting and searching (volume 3) , 1973 .

[3]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[4]  Donald E. Knuth,et al.  The art of computer programming: V.1.: Fundamental algorithms , 1997 .

[5]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[6]  P. Flajolet On approximate counting , 1982 .

[7]  N. Alon,et al.  il , , lsoperimetric Inequalities for Graphs , and Superconcentrators , 1985 .

[8]  N. Alon Eigenvalues and expanders , 1986, Comb..

[9]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, WG.

[10]  J. Spencer Ten lectures on the probabilistic method , 1987 .

[11]  Vijay V. Vazirani,et al.  Matching is as easy as matrix inversion , 1987, STOC.

[12]  Richard M. Karp,et al.  Efficient Randomized Pattern-Matching Algorithms , 1987, IBM J. Res. Dev..

[13]  M. Luby,et al.  Polytopes, permanents and graphs with large factors , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[14]  Mark Jerrum,et al.  Approximating the Permanent , 1989, SIAM J. Comput..

[15]  Martin E. Dyer,et al.  A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies , 1989, STOC.

[16]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, International Workshop on Graph-Theoretic Concepts in Computer Science.

[17]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[18]  Richard M. Karp,et al.  An introduction to randomized algorithms , 1991, Discret. Appl. Math..

[19]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[20]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[21]  Mark Jerrum,et al.  A Very Simple Algorithm for Estimating the Number of k-Colorings of a Low-Degree Graph , 1995, Random Struct. Algorithms.

[22]  Mechthild Stoer,et al.  A simple min-cut algorithm , 1997, JACM.

[23]  David S. Williams Weighing the odds : a course in probability and statistics , 2001 .

[24]  L. Shepp Probability Essentials , 2002 .