A Faster FPT Algorithm for Bipartite Contraction

Abstract

The Bipartite Contraction problem is to decide, given a graph G and a parameter k, whether we can can obtain a bipartite graph from G by at most k edge contractions. The fixed-parameter tractability of the problem was shown by Heggernes et al. [13], with an algorithm whose running time has double-exponential dependence on k. We present a new randomized FPT algorithm for the problem, which is both conceptually simpler and achieves an improved \(2^{O(k^2)} n m\) running time, i.e., avoiding the double-exponential dependence on k. The algorithm can be derandomized using standard techniques.KeywordsBipartite GraphSpan ForestEdge ContractionValid PartitionImportant SeparatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.