On the Complexity of the Discrete Fréchet Distance under L 1 and L ∞
نویسندگان
چکیده
We study the decision tree complexity of the discrete Fréchet distance (decision version) under the L1 and L∞ metrics over R. While algorithms for the Euclidean (L2) discrete Fréchet distance were studied extensively, the problem in other metrics such as L1 and L∞ seems to be much less investigated. For the L1 discrete Fréchet distance in R we present a 2d-linear decision tree with depth O(n log n), for any constant d. For the L∞ discrete Fréchet distance in R we present a 2-linear decision tree with depth O(n log n), for any constant d. We hope that these near-linear depth decision trees will motivate the study of the problem in these metrics and, in particular, will lead to the development of improved algorithms.
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