Related papers: Isometric Words based on Swap and Mismatch Distanc…
For non-empty sets X we define notions of distance and pseudo metric with values in a partially ordered set that has a smallest element $\theta $. If $h_X$ is a distance in $X$ (respectively, a pseudo metric in $X$), then the pair $(X,h_X)$…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
We define and investigate the Fr\'{e}chet edit distance problem. Given two polygonal curves $\pi$ and $\sigma$ and a threshhold value $\delta>0$, we seek the minimum number of edits to $\sigma$ such that the Fr\'{e}chet distance between the…
Cross-lingual word embeddings encode the meaning of words from different languages into a shared low-dimensional space. An important requirement for many downstream tasks is that word similarity should be independent of language - i.e.,…
Given a string $\sigma$ over alphabet $\Sigma$ and a grammar $G$ defined over the same alphabet, how many minimum number of repairs: insertions, deletions and substitutions are required to map $\sigma$ into a valid member of $G$ ? We…
Text attribute transfer aims to automatically rewrite sentences such that they possess certain linguistic attributes, while simultaneously preserving their semantic content. This task remains challenging due to a lack of supervised parallel…
Edit distance, also known as Levenshtein distance, is an essential way to compare two strings that proved to be particularly useful in the analysis of genetic sequences and natural language processing. However, edit distance is a discrete…
We show that the edit distance between two strings of length $n$ can be computed within a factor of $f(\epsilon)$ in $n^{1+\epsilon}$ time as long as the edit distance is at least $n^{1-\delta}$ for some $\delta(\epsilon) > 0$.
There exists a bijection between one stack sortable permutations --permutations which avoid the pattern 231-- and planar trees. We define an edit distance between permutations which is coherent with the standard edit distance between trees.…
We introduce the \textit{Asymptotic Hausdorff} lifting, denoted $\mathbb{AH}_{d}$, a general method for lifting an element-level metric $d$ to a (pseudo-) metric on sets, that captures asymptotic similarity in infinite domains equipped with…
The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F(p). This interpretation of the…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. In this paper we introduce the concept of twisted automorphisms, a notion of isomorphism up to a permutation of…
Lexical gaps are words that do not exist in certain languages. They pose challenges for building multilingual lexical resources, for machine translation, and for cross-lingual transfer. Existing lexical gap detection relies on human…
This research examines how well different methods measure semantic similarity, which is important for various software engineering applications such as code search, API recommendations, automated code reviews, and refactoring tools. While…
Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.
The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The edit distance function of the hereditary property, $\mathcal{H}$, is a function of $p\in[0,1]$ and is the…
Word and sentence embeddings are useful feature representations in natural language processing. However, intrinsic evaluation for embeddings lags far behind, and there has been no significant update since the past decade. Word and sentence…
We construct a binary minimal subshift whose words of length n form a connected subset of the Hamming graph for each n.
Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form xx', where x and x' are close to being identical. In their work, they…