Complexity Column

Approximation algorithm and limits of approximation is one of the major topics in algorithms, complexity theory, and computer science in general. The area uses multiple algorithmic techniques such as Semidefinite Programming (SDP), as well as advanced tools of proving inapproximabily, one of the most important of which is the PCP Theorem. The overall goal is, of course, to determine the best attainable approximability ration and provide an algorithm capable of achieving this ratio. Unconditional inapproximability results are generally very difficult, which prompted the use of the Unique Games Conjecture (UGC) introduced by S.Khot that posits the inapproxibality of a certain basic problem. The UGC, as well as the majority of the problems researchers are focusing on can be formulated withing the general framework of the Constraint Satisfaction Problem (CSP).