Treewidth Computation and Kernelization in the Parallel External Memory Model [chapter]

Riko Jacob, Tobias Lieber, Matthias Mnich
2014 Lecture Notes in Computer Science  
We present a randomized algorithm which computes, for any fixed k, a tree decomposition of width at most k of any input graph. We analyze it in the parallel external memory (PEM) model that measures efficiency by counting the number of cache misses on a multi-CPU private cache shared memory machine. Our algorithm has sorting complexity, which we prove to be optimal for a large parameter range. We use this algorithm as part of a PEM-efficient kernelization algorithm. Kernelization is a technique
more » ... for preprocessing instances of size n of NP-hard problems with a structural parameter κ by compressing them efficiently to a kernel, an equivalent instance of size at most g(κ). An optimal solution to the original instance can then be recovered efficiently from an optimal solution to the kernel. Our main results here is an adaption of the linear-time randomized protrusion replacement algorithm by Fomin et al. (FOCS 2012). In particular, we obtain efficient randomized parallel algorithms to compute linear kernels in the PEM model for all separable contraction-bidimensional problems with finite integer index (FII) on apex minor-free graphs, and for all treewidth-bounding graph problems with FII on topological minor-free graphs.
doi:10.1007/978-3-662-44602-7_7 fatcat:tjzng5qyhbbmtmyc5c4chgqeue