Semi-Exact Exponential-Time Algorithms: An Experimental Study

The last decade witnessed an increased interest in exact and parameterized exponential-time algorithms for NP - hard problems. The hardness of polynomial-time approximation of many intractable problems motivated the work on fixed-parameter approximation where polynomial-time is relaxed into FPT -time as long as improved approximation is obtained, most often requiring constant ratio bounds. In this paper we move a step further by investigating the practicality of exponential time approximation (versus FPT-time) as long as obtained solutions are within an additive parameter. The running time of such algorithm would be reduced by some function (factor) of the same parameter. The objective is to obtain a cost-effective trade-off between reduced running time and quality of approximation while providing provably near optimal solutions. We present experimental studies of two problems: Dominating Set and Vertex Cover. Our experiments show that semi-exact algorithms are indeed very promising.