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Consider a vertex-weighted graph $G$ with a source $s$ and a target $t$.Tracking Paths requires finding a minimum weight set of vertices (trackers)such that the sequence of trackers in each path from $s$ to $t$ is unique. Inthis work, we derive a factor $6$-approximation algorithm for Tracking Paths inweighted graphs and a factor $4$-approximation algorithm if the input isunweighted. This is the first constant factor approximation for this problem.While doing so, we also study approximation of the closely related $r$-FaultTolerant Feedback Vertex Set problem. There, for a fixed integer $r$ and agiven vertex-weighted graph $G$, the task is to find a minimum weight set ofvertices intersecting every cycle of $G$ in at least $r+1$ vertices. We give afactor $\mathcal{O}(r)$ approximation algorithm for $r$-Fault Tolerant FeedbackVertex Set if $r$ is a constant.

Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set