Research Interest

My research focuses on Visualized Algorithm Engineering that combines Algorithm Engineering with Visualization. Particularly, I am interested in Graph partitioning problems (Network partitioning or clustering problems). My Ph.D. dissertation titled “Visualized Algorithm Engineering on Two Graph Partitioning Problems” is published on SMU Scholar.

For more detail, here is my research statement. This page shows a list of related conferences, workshops, and publications.

Research Topics

1. Bipartite Grid Partitioning of a Random Geometric Graph

   We investigate the efficient computation of partitioning a Random Geometric Graph (RGG) into a limited number of densely packed bipartite subgraphs. The study focuses on the collection of subgraphs each individually having similar size and structure and the union employing most (e.g. over 85%) of the vertices. The residual vertices we seek to minimize are attributed to the inherent variations in densities of the randomly placed vertices and to any shortcomings of our greedy algorithms. RGGs have been extensively employed to model the deployment of numerous instances of Wireless Sensor Networks (WSNs). The corresponding application of our research is the backbone determination of a WSN.

2. Hierarchical Maximum Concurrent Flow Problem

   We review the foundations of a hierarchical network par- titioning method based on the fundamental concept of density (i.e., sparse cuts separating dense components) and implemented via a duality to peer-to-peer network flow between all node pairs.

3. Primordial Forest of Natural Numbers

   In SIAM Review 10, page 273, my superviosr Professor David W. Matula described a bijection between any natural number and the set of topological rooted trees; the number is called the Matula number of the rooted tree. By exploring the tree structure of Matula Number, we discovered a new relation `ip_jRRjp_i` (function `p_i` denotes as the `i^{th}` prime) which partitions the set of all natural numbers into equivalence classes in one to one correspondence with the forest of all finite trees.

   We term the relation `ip_jRRjp_i` the primordial relation over the natural numbers and the partition into clusters of natural numbers the primordial forest.

Conferences & Workshops

1. 26th IEEE Symposium on Computer Arithmetic (Arith26)

   When: June 10^th ~ June 12^th, 2019    Location: Kyoto, Japan    Resources: Paper, Slides

   Since 1969, the ARITH symposia have served as the flagship conference for presenting scientific work on the latest research in computer arithmetic. I published the paper “Precise and Concise Graphical Representation of the Natural Numbers”.

2. SIAM Workshop on Network Science (NS16; NS17; NS18)

   When: July 12^th ~ July 13^th, 2018    Location: Portland, Oregon, USA    Resources: Abstract, All programs
           When: July 13^th ~ July 14^th, 2017    Location: Pittsburgh, Pennsylvania, USA    Resources: Abstract, All programs
           When: July 15^th ~ July 16^th, 2016    Location: Boston, Massachusetts, USA    Resources: Abstract, All programs

   Network science studies the mathematical structure of the graphs that arise in these diverse fields, and the design, analysis, and applications of algorithms that compute with and on them. The goal of the SIAM Network Science workshop is to promote cross-fertilization among the communities that study and apply networks and graphs, both inside and outside SIAM. I presented topic on “Partitioning Random Geometric Graphs into Bipartite Backbones” to NS16 workshop in Boston; “The Evolution of Flow-Based Hierarchy in Networks” in NS17; “Backbone Structure of Hierarchical Network Partitioning” in NS18.

3. The 13th International Conference on Distributed Computing in Sensor Systems (DCOSS 2017)

   When: June 5^th ~ June 7^th, 2017    Location: Ottawa, Ontario, Canada    Resources: Paper, Slides

   The conference is intended to cover several aspects of distributed computing in sensor systems such as high level abstractions and models, systematic design methodologies, signal and information processing, algorithms, analysis and applications. In DCOSS 2017 conference, I gave a speech on topic "Bipartite Grid Partitioning of a Random Geometric Graph" at University of Ottawa.

4. The 17th International Conference on RANDOM STRUCTURES AND ALGORITHMS (RS&A2015)

   When: July 27^th ~ July 31^st, 2015    Location: Pittsburgh, Pennsylvania, USA    Resources: Program

   The conference, organized biennially since 1983, brings together probabilists, discrete mathematicians and theoretical computer scientists working in probabilistic methods, random structures and randomized algorithms. I gave contributed talk on topic “Bipartite Subgraphs of Random Geometric Graphs” at Carnegie Mellon University.

5. The Sixth SIAM Workshop on Combinatorial Scientific Computing (CSC14)

   When: July 21^st ~ July 23^rd, 2014    Location: Lyon, France    Resources: Paper, Proceeding

   The workshop focuses on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. In CSC14, I presented topic on “Partitioning RGG’s into disjoint (1-ε) dominant bipartite subgraphs” at École Normale Supérieure de Lyon.