Strong computational lower bounds via parameterized complexity

Strong computational lower bounds via parameterized complexity

We develop new techniques for deriving strong computational lower bounds for a class of well-known NP-hard problems. This class includes weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(nk) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely coll...

Strict lower and upper bounds on iterative computational complexity

Computational complexity lower bounds of certain discrete Radon transform approximations

For the computational model where only additions are allowed, the Ω(n log n) lower bound on operations count with respect to image size n × n is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proo...

Two Lower Bounds on Computational Complexity of Infinite Words

The most of the previous work on the complexity of in nite words has measured the complexity as descriptional one, i. e. an in nite word w had a \small" complexity if it was generated by a morphism or another simple machinery, and w has been considered to be \complex" if one needs to use more complex devices (gsm's) to generate it. In [J. Hromkovi c, J. Karhum aki, A. Lepist o: \Comparing des...

Upper and lower bounds on the computational complexity of ODEs

We investigate the computational complexity of the solution of y′ = f(t, y) when f : R → R is primitively recursive computable. In particular, we show that there is some f and initial conditions with complexity on the level E, n ≥ 3, of Grzegorczyk’s hierarchy, such that the complexity of the unique solution y does not collapse to the previous level E. As a corollary, we present some connection...