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arXiv · 1305.2743

A faster FPT algorithm for Bipartite Contraction

Sylvain Guillemot·Dániel Marx
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Abstract

The \textsc{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. 2011], 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.

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Sylvain Guillemot, Dániel Marx. 2013-09-04. A faster FPT algorithm for Bipartite Contraction. https://arxiv.org/abs/1305.2743

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