Fast FPT-Algorithms for Cleaning Grids

Abstract

We consider the problem that, given a graph G and a parameter k, asks whether the edit distance of G and a rectangular grid is at most k. We examine the general case where the edit operations are vertex/edge removals and additions. If the dimensions of the grid are given in advance, we give a parameterized algorithm that runs in 2^{O(logk· k)}+O(n ³) steps. In the case where the dimensions of the grid are not given we give a parameterized algorithm that runs in 2^O(logk·k)+O(k ²·n ³) steps. We insist on parameterized algorithms with running times where the relation between the polynomial and the non-polynomial part is additive. Our algorithm is based on the technique of kernelization. In particular we prove that for each version of the above problem there exists a kernel of size O(k ⁴).

This research was supported by the spanish CICYT project TIN-2004-07925 (GRAMMARS). The first author was partially supported by the Distinció per a la Promoció de la Recerca de la GC, 2002.