相关论文: Exact computation of the matching distance on 2-pa…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…

Let $\cal{P}$ be an affine invariant property of functions $\mathbb{F}_p^n \to [R]$ for fixed $p$ and $R$. We show that if $\cal{P}$ is locally testable with a constant number of queries, then one can estimate the distance of a function $f$…

We study modal separability for fixpoint formulae: given two mutually exclusive fixpoint formulae $\varphi,\varphi'$, decide whether there is a modal formula $\psi$ that separates them, that is, that satisfies…

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…

A recent work by Lesnick and Wright proposed a visualisation of $2$D persistence modules by using their restrictions onto lines, giving a family of $1$D persistence modules. We give a constructive proof that any $1$D persistence module with…

Multiparameter persistence modules come up naturally in topological data analysis and topological robotics. Given a metric graph $(X,\delta)$, the second configuration space of $(X,\delta)$ with proximity parameters (for example, the…

We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4),…

To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…

Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…

An important problem in the field of Topological Data Analysis is defining topological summaries which can be combined with traditional data analytic tools. In recent work Bubenik introduced the persistence landscape, a stable…

It is well-known that parallel manipulators are prone to singularities. However, there is still a lack of distance evaluation functions, referred to as metrics, for computing the distance between two 3-RPR configurations. The proposed…

Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

This paper extends the problem of 2-dimensional palindrome search into the area of approximate matching. Using the Hamming distance as the measure, we search for 2D palindromes that allow up to $k$ mismatches. We consider two different…

Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…

We study the theoretical complexity of simulated tempering for sampling from mixtures of log-concave components differing only by location shifts. The main result establishes the first polynomial-time guarantee for simulated tempering…

The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for…

Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can…

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…