Parameterized Fine-Grained Reductions [article]

Elli Anastasiadi, Antonis Antonopoulos, Aris Pagourtzis, Stavros Petsalakis
2019 arXiv   pre-print
During recent years the field of fine-grained complexity has bloomed to produce a plethora of results, with both applied and theoretical impact on the computer science community. The cornerstone of the framework is the notion of fine-grained reductions, which correlate the exact complexities of problems such that improvements in their running times or hardness results are carried over. We provide a parameterized viewpoint of these reductions (PFGR) in order to further analyze the structure of
more » ... provable problems and set the foundations of a unified methodology for extending algorithmic results. In this context, we define a class of problems (FPI) that admit fixed-parameter improvements on their running time. As an application of this framework we present a truly sub-quadratic fixed-parameter algorithm for the orthogonal vectors problem. Finally, we provide a circuit characterization for FPI to further solidify the notion of improvement.
arXiv:1902.05529v1 fatcat:b2migtkxfvgajevtpkja7az75q