Relating the Time Complexity of Optimization Problems in Light of the ExponentialTime Hypothesis
Abstract
Obtaining lower bounds for NPhard 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($\cdot$) 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 NPhard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finitevalued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.
 Publication:

arXiv eprints
 Pub Date:
 June 2014
 arXiv:
 arXiv:1406.3247
 Bibcode:
 2014arXiv1406.3247J
 Keywords:

 Computer Science  Computational Complexity
 EPrint:
 This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the ExponentialTime Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 2529, 2014