Approximation Algorithms
and Hardness of Approximation
EECS 598 - Special Topics
Instructor: Euiwoong Lee
Most interesting optimization problems are NP-hard, so unless P = NP, there are no
polynomial time algorithms to find optimal solutions to such problems. Therefore, it is
natural and important to study approximation algorithms that compute approximately
optimal solutions with provable guarantees. Computational complexity can be also
extended to approximate optimization, and for many optimization problems, it is possible
to prove that even computing an approximately optimal solution remains NP-hard.
Approximation algorithms have been actively studied in both algorithms and complexity
theory, culminating in optimal approximation algorithms for some fundamental problems;
they achieve some approximation guarantees and no polynomial time algorithm can do
better under some complexity conjectures. The theory of approximation algorithms also
leads to beautiful connections between algorithms, complexity, and some areas of
mathematics. This course will provide an overview of these connections, stressing
techniques and tools required to prove both algorithms and complexity results.
A tentative list of topics: linear programming (LP) and semidefinite programming (SDP)
relaxations, primal-dual method, randomized rounding, metric embedding, probabilistically
checkable proofs, discrete Fourier analysis, and unique games conjecture.
Prerequisites: Graduate or senior standing, or permission of the instructor.
Recommended: EECS 203, EECS 281, EECS 376, Math 217, or equivalents.
