An approximation algorithm for a general class of multi-parametric optimization problems

Abstract In a widely-studied class of multi-parametric optimization problems, the objective value each solution is an affine function real-valued parameters. Then, goal to provide optimal set, i.e., set containing for non-parametric problem obtained by fixing parameter vector. For many however, minimum cardinality can contain super-polynomially solutions. Consequently, no polynomial-time exact algorithms exist these problems even if $$\textsf {P}=\textsf {NP}$$ P=NP . We propose approximation method that applicable general and outputs solutions with polynomial in instance size inverse guarantee. This lifts their parametric version provides guarantee arbitrarily close algorithm problem. If be solved exactly time or FPTAS available, our FPTAS. Further, we show that, any given guarantee, is, general, not $$\ell $$ xmlns:mml="http://www.w3.org/1998/Math/MathML">ℓ -approximable natural number less equal parameters, discuss applications results classical combinatorial optimizations problems. particular, obtain s - t -cut problem, knapsack as well maximization independence systems