Discretely Following a Curve
نویسنده
چکیده
Finding the similarity between paths is an important problem that comes up in many areas such as 3D modeling, GIS applications, ordering, and reachability. Given a set of points S, a polygonal curve P , and an ε > 0, the discrete set-chain matching problem is to find another polygonal curve Q such that the nodes of Q are points in S and dF (P,Q) ≤ ε. Here, dF is the discrete Fréchet distance between the two polygonal curves. For the first time we study the set-chain matching problem based on the discrete Fréchet distance rather than the continuous Fréchet distance. We further extend the problem based on unique or non-unique nodes and on limiting the number of points used. We prove that three of the variations of the set-chain matching problem are NP-complete. For the version of the problem that we prove is polynomial, we give the optimal substructure and the recurrence for a dynamic programming solution.
منابع مشابه
Scheduling Problem with Discretely Compressible Release Dates
In this paper, we address the scheduling model with discretely compressible release dates, where processing any job with a compressed release date incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible release dates to minimize the sum of makespan plus total compression cost. We show its NP-hardness, and design an approximation algori...
متن کاملA Trace Formula for Varieties over a Discretely Valued Field
We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety X over a complete discretely valued field K with perfect residue field k. If K has characteristic zero, we extend the definition to arbitrary K-varieties using Bittner’s presentation of the Grothendieck ring and a process of Néron smoothening of pairs of varieties. The motivic Serre invariant can be considered...
متن کاملOn a family of test statistics for discretely observed diffusion processes
Let Xt, t ∈ [0, T ], be a d-dimensional diffusion process solution of the following stochastic differential equation dXt = b(α,Xt)dt+σ(β,Xt)dWt, where functions b and σ are suitably regular and known up to the parameters α ∈ R and β ∈ R . The process Xt is discretely observed at times ti, such that ti − ti−1 = ∆n < ∞ for 1 ≤ i ≤ n. The asymptotic scheme adopted in this paper is the following: T...
متن کاملTractable Clustering of Data on the Curve Manifold
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e. each data point is a function of some variable such as time and the function is discretely sampled. The naive treatment of functional data as traditional multivariate data can lead to poor performance since the algorithms are ignoring the correlation in ...
متن کاملA Logarithmic Interpretation of Edixhoven’s Jumps for Jacobians
Let A be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the Néron model of A that measures the behaviour of the Néron model under tame base change. We interpret the jumps in this filtration in terms of lattices of logarithmic differential forms in the case where A is the Jacobian of a curve C, and we give a compact explicit formula ...
متن کامل