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We initiate the study of spanners under the Hausdorff and Fr\'echetdistances. We show that any $t$-spanner of a planar point-set $S$ is a$\frac{\sqrt{t^2-1}}{2}$-Hausdorff-spanner and a$\min\{\frac{t}{2},\frac{\sqrt{t^2-t}}{\sqrt{2}}\}$-Fr\'echet spanner. We alsoprove that for any $t > 1$, there exist a set of points $S$ and an$\varepsilon_1$-Hausdorff-spanner of $S$ and an$\varepsilon_2$-Fr\'echet-spanner of $S$, where $\varepsilon_1$ and$\varepsilon_2$ are constants, such that neither of them is a $t$-spanner.

Spanners under the Hausdorff and Fr\'echet Distances