
Random projections and sampling algorithms for clustering of highdimensional polygonal curves
We study the center and median clustering problems for highdimensional ...
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Fast Fencing
We consider very natural "fence enclosure" problems studied by Capoyleas...
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Approximating (k,ℓ)Median Clustering for Polygonal Curves
In 2015, Driemel, Krivošija and Sohler introduced the (k,ℓ)median probl...
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FRESH: Fréchet Similarity with Hashing
Massive datasets of curves, such as time series and trajectories, are co...
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The kFréchet distance
We introduce a new distance measure for comparing polygonal chains: the ...
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SETH Says: Weak Fréchet Distance is Faster, but only if it is Continuous and in One Dimension
We show by reduction from the Orthogonal Vectors problem that algorithms...
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On Variants of Facility Location Problem with Outliers
In this work, we study the extension of two variants of the facility loc...
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Similarity of Polygonal Curves in the Presence of Outliers
The Fréchet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently occurring phenomenon in practice, a robust variant of Fréchet distance is required which absorbs outliers. We study such a variant here. In this modified variant, our objective is to minimize the length of subcurves of two polygonal curves that need to be ignored (MinEx problem), or alternately, maximize the length of subcurves that are preserved (MaxIn problem), to achieve a given Fréchet distance. An exact solution to one problem would imply an exact solution to the other problem. However, we show that these problems are not solvable by radicals over Q and that the degree of the polynomial equations involved is unbounded in general. This motivates the search for approximate solutions. We present an algorithm, which approximates, for a given input parameter δ, optimal solutions for the and problems up to an additive approximation error δ times the length of the input curves. The resulting running time is upper bounded by O(n^3/δ(n/δ)), where n is the complexity of the input polygonal curves.
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