8 citations · 30 across the 15 of their papers we have counts for
17 papers
A note on Global Positioning System (GPS) and Euclidean distance matrices
A. Y. Alfakih
Let be an Euclidean distance matrix (EDM) with embedding dimension ; and let be a given vector. In this note, we consider the problem of finding a v…
Single Element Error Correction/ in a Euclidean Distance Matrix
Abdo Alfakih, Woosuk L. Jung, Henry Wolkowicz +1
We consider the \emph{exact} error correction of a noisy Euclidean distance matrix, EDM, where the elements are the squared distances between points in . For our problem w…
Exact Solutions for the NP-hard Wasserstein Barycenter Problem using a Doubly Nonnegative Relaxation and a Splitting Method
Woosuk L. Jung, Henry Wolkowicz
The so-called \emph{simplified} Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of given sets, each set consis…
On the Colin de Verdiere graph number and penny graphs
A. Y. Alfakih
The Colin de Verdiere number of graph G, denoted by μ(G), is a spectral invariant of G that is related to some of its topological properties. For example, μ(G) \leq 3 iff G is plan…
On Theorems of Sinajova, Rankin and Kuperberg Concerning Spherical Point Configurations
A. Y. Alfakih
This note presents simple linear algebraic proofs of theorems due to Sinajova, Rankin and Kuperberg concerning spherical point configurations. The common ingredient in these proofs…
On Unit Spherical Euclidean Distance Matrices Which Differ in One Entry
A. Y. Alfakih
A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entries can be realized as the interpoint (squared) Euclidean distances of n points on a unit sphere. In this p…
On Representations of Graphs as Two-Distance Sets
A. Y. Alfakih
Let a \neq b be two positive scalars. A Euclidean representation of a simple graph G in R^r is a mapping of the nodes of G into points in R^r such that the squared Euclidean distan…
On yielding and jointly yielding entries of Euclidean distance matrices
A. Y. Alfakih
An matrix D is a Euclidean distance matrix (EDM) if there exist in some Euclidean space such that for all $i,j=1,\ldots,…
Universal Rigidity of Bar Frameworks via the Geometry of Spectrahedra
A. Y. Alfakih
A bar framework (G,p) in dimension r is a graph G whose vertices are points p^1,...,p^n in R^r and whose edges are line segments between pairs of these points. Two frameworks (G,p)…
Graph connectivity and universal rigidity of bar frameworks
A. Y. Alfakih
Let be a graph on nodes. In this note, we prove that if is -vertex connected, , then there exists a configuration in general position in $…
On Farkas Lemma and Dimensional Rigidity of Bar Frameworks
A. Y. Alfakih
We present a new semidefinite Farkas lemma involving a side constraint on the rank. This lemma is then used to present a new proof of a recent characterization, by Connelly and Gor…
On affine motions and universal rigidity of tensegrity frameworks
A. Y. Alfakih, Viet-Hang Nguyen
Recently, Alfakih and Ye [Lin. Algebra Appl. 438:31--36, 2013] proved that if an -dimensional bar framework on nodes in general position in admits a…
A Remark on the Manhattan Distance Matrix of a Rectangular Grid
A. Y. Alfakih
Consider the Quadratic Assignment Problem (QAP): given two matrices A and D, minimize {trace AXDX^T: X is a permutation matrix}. New lower bounds were obtained recently (Mittelmann…
On stress matrices of chordal bar frameworks in general position
A. Y. Alfakih
A bar framework in R^r, denoted by G(p), is a simple connected graph G whose vertices are points p^1,...,p^n in R^r that affinely span R^r, and whose edges are line segments betwee…
Universal rigidity of bar frameworks in general position: a Euclidean distance matrix approach
A. Y. Alfakih
A configuration p in r-dimensional Euclidean space is a finite collection of labeled points p^1,p^2,...,p^n in R^r that affinely span R^r. Each configuration p defines a Euclidean…
On affine motions and bar frameworks in general position
A. Y. Alfakih, Yinyu Ye
A configuration p in r-dimensional Euclidean space is a finite collection of points (p^1,...,p^n) that affinely span R^r. A bar framework, denoted by G(p), in R^r is a simple graph…
Toward the Universal Rigidity of General Frameworks
Abdo Y. Alfakih, Nicole Taheri, Yinyu Ye
Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admi…