Research Statement
Many important problems in modern mathematics involve the understanding of graphs. Their structure encodes information useful for countless applications and presents interesting questions of pure theoretic interest. Much of complexity theory relies upon different classes of graphs to define the most important problems. Many tools and techniques have been developed to analyze graphs: their invariants, automorphisms, and their existence under certain conditions. My goal is to combine modern proof techniques with computational methods to solve these unanswered questions, including the existence of certain strongly-regular graphs, space-bounded algorithms for reachability, and variants of the Reconstruction Conjecture.
Papers
- Stephen G. Hartke, Hannah Kolb, Jared Nishikawa, Derrick Stolee, "Automorphism groups of a graph and a vertex-deleted subgraph," under submission, September 2009.
- Derrick Stolee, Chris Bourke, N.V. Vinodchandran, "A log-space algorithm for planar DAGs with few sources," Electronic Colloquium of Computational Complexity, June 2009.
Presentations
- "A log-space algorithm for planar DAGs with few sources,"
Discrete Math Seminar, January 27, 2009.
(with Chris Bourke, and N.V. Vinodchandran) -
"Using Wireless Sensor Networks for Low-Cost Fast-Installation Three-dimensional Environment Modelling,"
Wireless Sensor Networks, December , 2008.
(with Dan Cromer, Kurt Larson, and Zach Miller) - "(3,1)-Subspace Intersection Representations of Graphs,"
GSS, October 22, 2008.
(with James Carraher, Travis Johnston, and Stephen Hartke) - "Minimum Rectilinear Partitioning,"
GSCC 2008, University of California-Davis. April 12, 2008. - "A Multi-Dimensional Spatial Cache for Distributed Decision Support Systems,"
Undergraduate Thesis Defense, April 16, 2007.
Current Projects
- Reconstructing Separable Graphs
Managing the effect leaves have when reconstructing separable graphs. - Deletion Relations of Graphs
Finding the groups that can appear as automorphism groups of a graph and a vertex-deleted subgraph. - Computational Searches
- Low-order counterexamples to edge reconstruction
- Certificate polynomials to insolvable SAT instances
- Distributing McKay's isomorph-free generation algorithm
-
Graph Isomorphism Complexity
McKay'snauty, Babai & Luk, Quantum
Derrick Stolee
Derrick
is a graduate student in the Joint Mathematics and Computer Science
Ph.D. program at the University of Nebraska-Lincoln. Research areas
include Graph Theory, Graph Algorithms, and Computational Complexity.
