Fast Parallel Fixed-Parameter Algorithms via Color Coding
Abstract
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use of the parallel hardware present in modern computers. We show that parallel fixed-parameter algorithms do not only exist for numerous parameterized problems from the literature -- including vertex cover, packing problems, cluster editing, cutting vertices, finding embeddings, or finding matchings -- but that there are parallel algorithms working in \emph{constant} time or at least in time \emph{depending only on the parameter} (and not on the size of the input) for these problems. Phrased in terms of complexity classes, we place numerous natural parameterized problems in parameterized versions of AC. On a more technical level, we show how the \emph{color coding} method can be implemented in constant time and apply it to embedding problems for graphs of bounded tree-width or tree-depth and to model checking first-order formulas in graphs of bounded degree.
Cite
@article{arxiv.1509.06984,
title = {Fast Parallel Fixed-Parameter Algorithms via Color Coding},
author = {Max Bannach and Christoph Stockhusen and Till Tantau},
journal= {arXiv preprint arXiv:1509.06984},
year = {2015}
}