Seminar: An approximation algorithm for zero forcing

Speaker: Owen Zhang, TMU

Title: An approximation algorithm for zero forcing

Abstract: We give an algorithm that finds a zero forcing set which approximates the optimal size by a factor of $\mathrm{pw}(G)+1$, where $\mathrm{pw}(G)$ is the pathwidth of $G$. The algorithm requires a path decomposition of $G$, and given this it runs in $O(nm)$ time, where $n$ and $m$ are the order and size of the graph, respectively. This is the first zero forcing algorithm with a guarantee on both the approximation ratio and on the run-time. As a corollary, we obtain a new upper bound on the zero forcing number in terms of the fort number and the pathwidth. The algorithm is based on a correspondence between zero forcing sets and forcing arc sets.  This correspondence leads to a new bound on the zero forcing number in terms of vertex cuts, and to new, short proofs for known bounds on the zero forcing number. 

This is a joint work with Ben Cameron, Jeannette Janssen, and Rogers Mathew.