Limits of Approximation Algorithms: PCPs and Unique Games (DIMACS Tutorial Lecture Notes)

TL;DR

This paper discusses the theoretical limits of approximation algorithms, focusing on Probabilistically Checkable Proofs (PCPs) and the Unique Games Conjecture, highlighting their implications for computational hardness and algorithm design.

Contribution

It provides an overview of the state-of-the-art in PCPs and Unique Games, emphasizing their role in understanding the boundaries of approximation algorithms.

Findings

PCPs are central to hardness of approximation results.

The Unique Games Conjecture influences many inapproximability results.

The tutorial summarizes key open problems and recent advances in the field.

Abstract

These are the lecture notes for the DIMACS Tutorial "Limits of Approximation Algorithms: PCPs and Unique Games" held at the DIMACS Center, CoRE Building, Rutgers University on 20-21 July, 2009. This tutorial was jointly sponsored by the DIMACS Special Focus on Hardness of Approximation, the DIMACS Special Focus on Algorithmic Foundations of the Internet, and the Center for Computational Intractability with support from the National Security Agency and the National Science Foundation. The speakers at the tutorial were Matthew Andrews, Sanjeev Arora, Moses Charikar, Prahladh Harsha, Subhash Khot, Dana Moshkovitz and Lisa Zhang. The sribes were Ashkan Aazami, Dev Desai, Igor Gorodezky, Geetha Jagannathan, Alexander S. Kulikov, Darakhshan J. Mir, Alantha Newman, Aleksandar Nikolov, David Pritchard and Gwen Spencer.