Related papers: Towards Normalizing the Edit Distance Using a Gene…
We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we…
Trace reconstruction considers the task of recovering an unknown string $x \in \{0,1\}^n$ given a number of independent "traces", i.e., subsequences of $x$ obtained by randomly and independently deleting every symbol of $x$ with some…
Natural language processing is an important discipline with the aim of understanding text by its digital representation, that due to the diverse way we write and speak, is often not accurate enough. Our paper explores different…
We study the fundamental problem of approximating the edit distance of two strings. After an extensive line of research led to the development of a constant-factor approximation algorithm in almost-linear time, recent years have witnessed a…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance. For the gap edit distance problem, we give an $\tilde{O}(\frac{n}{k}+k^2)$-time greedy…
Kondo et al. (DS 2014) proposed methods for computing distances between unordered rooted trees by transforming an instance of the distance computing problem into an instance of the integer programming problem. They showed that the tree edit…
We introduce a new distance and we use it to parameter estimation purposes. We observe how it operates and we use in its place the usual methods of estimation which we call the methods of the new approach. We realize that we obtain a…
The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
In this paper we provide a new locally consistent decomposition of strings. Each string $x$ is decomposed into blocks that can be described by grammars of size $\widetilde{O}(k)$ (using some amount of randomness). If we take two strings $x$…
We present a new method for image feature-extraction which is based on representing an image by a finite-dimensional vector of distances that measure how different the image is from a set of image prototypes. We use the recently introduced…
Among various distance functions for graphs, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this…
The Graph Edit Distance (GED) problem, which aims to compute the minimum number of edit operations required to transform one graph into another, is a fundamental challenge in graph analysis with wide-ranging applications. However, due to…
Statement autoformalization, the automated translation of statements from natural language into formal languages, has become a subject of extensive research, yet the development of robust automated evaluation metrics remains limited.…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
The edit distance between two graphs on the same vertex set is defined to be the size of the symmetric difference of their edge sets. The edit distance function of a hereditary property, $\mathcal{H}$, is a function of $p$, and measures,…
The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical…
Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to predict the native structure of proteins. However, NMR machines are only able to report approximate and partial distances between pair of atoms. To build the…
We define edit distance for hierarchically structured data compatible with the hierarchical multi-instance learning paradigm. Example of such data is dataset represented in JSON format where inner Array objects are interpreted as unordered…