eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-19
224
235
10.4230/LIPIcs.IPEC.2015.224
article
Fast Parallel Fixed-parameter Algorithms via Color Coding
Bannach, Max
Stockhusen, Christoph
Tantau, Till
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 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 constant time or at least in time 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^0. On a more technical level, we show how the 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol043-ipec2015/LIPIcs.IPEC.2015.224/LIPIcs.IPEC.2015.224.pdf
color coding
parallel computation
fixed-parameter tractability
graph packing
cutting $ell$ vertices
cluster editing
tree-width
tree-depth,