The metric dimension of a graph is the smallest number of nodes required to identify all other
nodes uniquely based on shortest path distances. Applications of metric dimension include …

Numerous data analysis and data mining techniques require that data be embedded in a
Euclidean space. When faced with symbolic datasets, particularly biological sequence data …

A graph $G=(V,E)$ with geodesic distance $d(\cdot,\cdot)$ is said to be resolved by a non-empty
subset $R$ of its vertices when, for all vertices $u$ and $v$, if $d(u,r)=d(v,r)$ for each $r…

Let G be a graph with vertex set V ( G ) , and let d ( x , y ) denote the length of a shortest path
between nodes x and y in G . For a positive integer k and for distinct x , y ∈ V ( G ) , let d k ( x …

Symbolic data plays a prominent role in a variety of fields. This is particularly true in modern
biology where sequence information has become an indispensable tool. In contrast, most …

A subset of vertices in a graph is called resolving when the geodesic distances to those vertices
uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of …

In this manuscript, we provide a concise review of the concept of metric dimension for both
deterministic as well as random graphs. Algorithms to approximate this quantity, as well as …

Systems of interest in bioinformatics and computational biology tend to be large, complex,
interdependent, and stochastic. As our ability to collect sequence data at finer resolutions …

Many machine learning techniques such as k-nearest neighbors (KNNs) and support vector
machines (SVMs) require examples to be mapped to numerical feature vectors. Principal …

Identifying the source of a spread in a network, often referred to as the patient-zero problem,
is a difficult task when only given the subgraph of infected nodes. Since 2011, several …