Not available in 2015/16
MG4A7      Half Unit
Solving Unsolvable Problems: NP- completeness and how to cope with it

This information is for the 2015/16 session.

Teacher responsible

Prof Gregory Sorkin NAB 3.19


This course is available on the MSc in Management Science (Decision Sciences) and MSc in Management Science (Operational Research). 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.

Course content

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.

Indicative reading

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) in the main exam period.
Coursework (15%) in the LT.

Key facts

Department: Management

Total students 2014/15: Unavailable

Average class size 2014/15: Unavailable

Controlled access 2014/15: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Team working
  • Problem solving
  • Communication
  • Application of numeracy skills
  • Specialist skills