Before revision:  Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given \epsilon > 0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Fr\'echet distance between the input and output polylines is at most \epsilon .
After revision:  Interestingly, no previous authors studied line simplification under these measures in its pure form, namely: for a given \varepsilon > 0, choose a minimum size subsequence of the vertices of the input such that the Hausdorff or Fr\'echet distance between the input and output polylines is at most \epsilon .