KAIST Discrete Math Seminar

Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection between these different frameworks. In particular, whether Independent Set would be better approximable once allowed with subexponential-time or FPT-time is a central question. Recently, several independent results appeared regarding this question, implying negative answer toward the conjecture. They state that, for every 0<r<1, there is no r-approximation which runs in better than certain subexponential-function time. We outline the results in these papers and overview the important concepts and techniques used to obtain such results.