Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT(·) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation R such that SAT(R) can be solved at least as fast as any other NP-hard SAT(·) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MAX-ONES(Γ )) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP(∆)). With the help of these languages we relate MAX-ONES and VCSP to the exponential time hypothesis in several different ways.