Related papers: An Algorithm for Comparing Similarity Between Two …
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…
Comparative analysis of scalar fields in scientific visualization often involves distance functions on topological abstractions. This paper focuses on the merge tree abstraction (representing the nesting of sub- or superlevel sets) and…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at…
We study the number of distance queries needed to identify certain properties of a hidden tree $T$ on $n$ vertices. A distance query consists of two vertices $x,y$, and the answer is the distance of $x$ and $y$ in $T$. We determine the…
The \emph{distance-number} of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…
The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations.…
Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped…
Searching topological similarity between a pair of shapes or data is an important problem in data analysis and visualization. The problem of computing similarity measures using scalar topology has been studied extensively and proven useful…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine…