# On Flipping the Fr\'{e}chet distance

@inproceedings{Filtser2022OnFT, title={On Flipping the Fr\'\{e\}chet distance}, author={Omrit Filtser and Mayank Goswami and Joseph S. B. Mitchell and Valentin Polishchuk}, year={2022} }

The classical and extensively-studied Fréchet distance between two curves is deﬁned as an inf max , where the inﬁmum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a “ﬂipped” Fréchet measure deﬁned by a sup min – the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of “social distance” between two curves (or…

## References

SHOWING 1-10 OF 21 REFERENCES

### Why Walking the Dog Takes Time: Frechet Distance Has No Strongly Subquadratic Algorithms Unless SETH Fails

- Computer Science, Mathematics2014 IEEE 55th Annual Symposium on Foundations of Computer Science
- 2014

It is shown that the Fréchet distance cannot be computed in strongly subquadratic time, i.e., in time O(n2-δ) for any delta > 0.001-approximation, which means that finding faster algorithms is as hard as finding faster CNF-SAT algorithms, and the existence of a strongly subaquadratic algorithm can be considered unlikely.

### Approximability of the discrete Fréchet distance

- Computer Science, MathematicsJ. Comput. Geom.
- 2015

A new conditional lower bound is presented showing that strongly subquadratic algorithms for the discrete Frechet distance are unlikely to exist, even in the one-dimensional case and even if the solution may be approximated up to a factor of 1.399.

### Computing the Fréchet distance between two polygonal curves

- Computer Science, MathematicsInt. J. Comput. Geom. Appl.
- 1995

As a measure for the resemblance of curves in arbitrary dimensions we consider the so-called Frechet-distance, which is compatible with parametrizations of the curves. For polygonal chains P and Q…

### On the Fréchet distance of a set of curves

- MathematicsCCCG
- 2004

A measure for the resemblance of curves, Alt and Godau have considered the so-called Frechet distance 243, which is a continuous mapping of curves with values of "0/1$".

### Geodesic Fréchet distance inside a simple polygon

- Computer ScienceTALG
- 2010

An alternative to parametric search that applies to both the nongeodesic and geodesic Fréchet optimization problems is presented, based on a variant of red-blue intersections, which is appealing due to its elegance and practical efficiency when compared toParametric search.

### Approximation of Geometric Dispersion Problems

- MathematicsAlgorithmica
- 2001

This work gives a 2/3 approximation algorithm for one version of the geometric dispersion problem, which is strongly polynomial in the size of the input, i.e., its running time does not depend on the area of P .

### SETH Says: Weak Fréchet Distance is Faster, but only if it is Continuous and in One Dimension

- Computer Science, MathematicsSODA
- 2019

It is shown by reduction from the Orthogonal Vectors problem that algorithms with strongly subquadratic running time cannot approximate the Frechet distance between curves better than a factor 3 unless SETH fails, and an exact algorithm is provided to compute the weak Frechet Distance in linear time.

### Maximum Dispersion and Geometric Maximum Weight Cliques

- Mathematics, Computer ScienceAlgorithmica
- 2003

This paper presents algorithmic results for the case where vertices are represented by points in d-dimensional space, and edge weights correspond to rectilinear distances, and establishes a linear-time algorithm that finds an optimal solution.

### Computing Discrete Fréchet Distance ∗

- Computer Science, Economics
- 1994

A discrete variation of the Fréchet distance that provides good approximations of the continuous measure and can be efficiently computed using a simple algorithm is presented.