Oral Presentations and Performances: Session I
Project Type
Presentation
Project Funding and Affiliations
National Science Foundation
Faculty Mentor’s Full Name
Cory Palmer
Faculty Mentor’s Department
Mathematical Sciences
Abstract / Artist's Statement
The Gyárfás tree packing conjecture [1] states that any collection of trees (T1, T2, . . . , Ti) on 1, 2, . . . n vertices can be edge-disjointly packed into a complete graph on n vertices. Alternatively, this conjecture states that such a family of trees can be “glued” together to produce a complete graph on n vertices. Although many partial results are known (See Cisiński and Zak [2], Janzer and Montgomery [3], Balogh and Palmer [4]), ˙ the conjecture has remained open since 1970. This conjecture is computationally challenging, naively requiring superexponential number of computations. This paper will use different types of computations and optimizations to approach the problem. By writing serial, and parallel algorithms on both CPU and GPU architecture in the Python programming language, valid packings can be computed. This project will also leverage university research computing infrastructure to address the computational difficulty. Using these techniques and discovering further efficiencies, this paper will find that using parallel GPU workload, with memory balancing can go to a higher n than a serial CPU algorithm can. This project will also serve as a pilot to demonstrate how to use a research cluster and how efficient algorithms can be used to approach similar problems.
Category
Physical Sciences
Computing the Tree Packing Conjecture
UC 329
The Gyárfás tree packing conjecture [1] states that any collection of trees (T1, T2, . . . , Ti) on 1, 2, . . . n vertices can be edge-disjointly packed into a complete graph on n vertices. Alternatively, this conjecture states that such a family of trees can be “glued” together to produce a complete graph on n vertices. Although many partial results are known (See Cisiński and Zak [2], Janzer and Montgomery [3], Balogh and Palmer [4]), ˙ the conjecture has remained open since 1970. This conjecture is computationally challenging, naively requiring superexponential number of computations. This paper will use different types of computations and optimizations to approach the problem. By writing serial, and parallel algorithms on both CPU and GPU architecture in the Python programming language, valid packings can be computed. This project will also leverage university research computing infrastructure to address the computational difficulty. Using these techniques and discovering further efficiencies, this paper will find that using parallel GPU workload, with memory balancing can go to a higher n than a serial CPU algorithm can. This project will also serve as a pilot to demonstrate how to use a research cluster and how efficient algorithms can be used to approach similar problems.