Genesis of ETH and SETH

Abstract

Several researchers have found ETH (Exponential Time Hypothesis) and Strong ETH to be useful and proved matching lower bounds for several problems in P as well as NP based on these conjectures. In this talk, I will talk about the technical results that motivated these conjectures. Specifically, I will talk about the following results: if ETH is false then a number of other NP-complete problems (the class SNP) will also have subexponential time algorithms, and the complexity of k-SAT must keep increasing with k under ETH. While these results are old, the latter result is relatively less well-known and I hope that it might inspire more work along the lines.