##### Education

###### PH.D.

Computer Science

Kent State University

###### Master of Science

Computer Science

University of Zakho

###### Bachelor of Science

Computer Science

University of Duhok

##### Professional Experience

###### Director of Registrar's Office

Registrar's Office

University of Zakho

UoZ

###### Teaching Assistant

Computer Science Department

Kent State University

KSU

###### Software Developer and Graduate Assistant

Information Services \ Systems Development Department

Kent State University.

KSU

###### Chair

Computer Science Department

University of Zakho

UoZ

###### Coordinator

Computer Science Department

University of Zakho

UoZ

##### Interest

Design and analysis of algorithms, approximation algorithms, algorithms for large scale networks, algorithmic graph.

##### Publication Journal

###### Fast Approximation and Exact Computation of Negative Curvature Parameters of Graphs

Discrete & Computational Geometry (Volume: 65:856–892)

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. The main contribution of this paper is a new characterization of the hyperbolicity of graphs, via a new parameter which we call rooted insize. This characterization has algorithmic implications in the field of large-scale network analysis. A sharp estimate of graph hyperbolicity is useful, e.g., in embedding an undirected graph into hyperbolic space with minimum distortion (Verbeek and Suri, in Symposium on Computational Geometry, ACM, New York, 2014). The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm (with an additive constant 1) for computing the hyperbolicity of an n-vertex graph G = (V, E) in optimal time O(n2) (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space. We also show that a similar characterization of hyperbolicity holds for all geodesic metric spaces endowed with a geodesic spanning tree. Along the way, we prove that any complete geodesic metric space (X, d) has such a geodesic spanning tree

###### Slimness of graphs

Discrete Mathematics & Theoretical Computer Science (Volume: 21:3)

Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph G = (V, E), a geodesic triangle 4(x, y, z) with x, y, z ∈ V is the union P(x, y)∪P(x, z)∪P(y, z) of three shortest paths connecting these vertices. A geodesic triangle 4(x, y, z) is called δ-slim if for any vertex u ∈ V on any side P(x, y) the distance from u to P(x, z) ∪ P(y, z) is at most δ, i.e. each path is contained in the union of the δ-neighborhoods of two others. A graph G is called δ-slim, if all geodesic triangles in G are δ-slim. The smallest value δ for which G is δ-slim is called the slimness of G. In this paper, using the layering partition technique, we obtain sharp bounds on slimness of such families of graphs as (1) graphs with cluster-diameter ∆(G) of a layering partition of G, (2) graphs with tree-length λ, (3) graphs with tree-breadth ρ, (4) k-chordal graphs, AT-free graphs and HHD-free graphs. Additionally, we show that the slimness of every 4-chordal graph is at most 2 and characterize those 4-chordal graphs for which the slimness of every of its induced subgraph is at most 1.

##### Conference

###### Fast approximation and exact computation of negative curvature parameters of graphs.

Hungary, Budapest As Presenter

In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. Our main contribution in this note is a new characterization of hyperbolicity for graphs (and for complete geodesic metric spaces). This characterization has algorithmic implications in the field of large-scale network analysis, which was one of our initial motivations. A sharp estimate of graph hyperbolicity is useful, {e.g.}, in embedding an undirected graph into hyperbolic space with minimum distortion [Verbeek and Suri, SoCG'14]. The hyperbolicity of a graph can be computed in polynomial-time, however it is unlikely that it can be done in subcubic time. This makes this parameter difficult to compute or to approximate on large graphs. Using our new characterization of graph hyperbolicity, we provide a simple factor 8 approximation algorithm for computing the hyperbolicity of an n-vertex graph G=(V,E) in optimal time O(n^2) (assuming that the input is the distance matrix of the graph). This algorithm leads to constant factor approximations of other graph-parameters related to hyperbolicity (thinness, slimness, and insize). We also present the first efficient algorithms for exact computation of these parameters. All of our algorithms can be used to approximate the hyperbolicity of a geodesic metric space.