, approximating the value with a precision of c log log n digits (for any constant c ≥ 1) can be done in quasi-polynomial time. We consider the parameterized complexity of the problem, with the parameter being the number of pure strategies k of the player for which the minmax value is computed. We show

We introduce and analyze a simulation-based, approximate dynamic programming method for pricing complex American-style options, with a possibly high-dimensional underlying state space. We work within a finitely parameterized family of approximate value functions, and introduce a variant of value

. For instance, we prove that value symmetry is fixed-parameter tractable to break in the number of symmetries. Finally, we argue that parameterized complexity can be used to derive results about the approximability of constraint propagation.

O(n k) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k)n o(k) for any function f, even if we restrict the parameter values to be bounded by an arbitrarily small

Approximation of curves by parametric polynomials or rational curves needs a linkage between curve points and parameter values. The quality of the approximation is highly dependent on this a priori parameterization. This quality criterium can be measured when the curve is given by dense

-time approximation scheme (PTAS). The main contribution of this paper is to explore this program from the point of view of parameterized complexity. Problems of optimization are naturally parameterized by the parameter k = 1/ɛ. An optimization problem admits a PTAS if and only if there is an algorithm Φ, that, given

reasoning. Technically, every transition in a weighted automaton A has a cost, and the value A assigns to a finite word w is the sum of the costs on the transitions participating in the most expensive accepting run of A on w. We study parameterized weighted containment: given three weighted automata A, B

. Moreover, ecosystem models often become unstable for small changes in parameter values, and increasing complexity may not lead to increased stability. Here we consider alternative formulations for ecosystem models that try to represent complex interactions, such as the microbial loop, in simpler, less

Abstract not found

We introduce and analyze a simulation-based approximate dynamic programming method for pricing complex American-style options, with a possibly high-dimensional underlying state space. We work within a finitely parameterized family of approximate value functions, and introduce a variant of value