Prof Gregory Sorkin NAB 3.19

This course is available on the MSc in Applicable Mathematics, MSc in Management Science (Decision Sciences) and MSc in Operations Research & Analytics. This course is available with permission as an outside option to students on other programmes where regulations permit.

A level of mathematical sophistication, including comfort with proofs and familiarity with limits, permutations, factorials, binomial coefficients, and rudimentary probability including expectations and independence. If in doubt, please consult the instructor or attend the first lecture.

Many problems, from the "Travelling Salesman Problem" to train scheduling, are easy to state but hard to solve, in a mathematically well-defined sense. In practical operations research, though, one must solve such problems, and the issues involved are mathematically interesting. The course will introduce the underlying computational concepts (polynomial-time computation and NP-completeness); introduce canonical problem models including graph problems and formula satisfiability; and explore various ways of addressing these problems, including heuristics, randomized and approximation algorithms, average-case analysis, and relatively efficient exponential-time algorithms.

20 hours of lectures and 13 hours and 30 minutes of seminars in the LT. 2 hours of lectures in the ST.

Shmoys and Williamson, The Design of Approximation Algorithms (Cambridge Univ. Press book, free e-version)

Sinclair, Randomness and Computation (U.C. Berkeley lecture notes, by kind permission of the author)

Print books

Fomin and Kratsch, Exact Exponential Algorithms

Mitzenmacher and Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Exam (85%, duration: 2 hours and 30 minutes, reading time: 15 minutes) in the summer exam period.
Coursework (15%) in the LT.