Most of my work in this area is based on the discrete Frechet distance on polygonal curves.

Many diverse areas related to problem complexity in several models, randomness, constructions, etc.

Motivating students in theory by working on proving the hardness of specific games using Constraint Graph reductions and standard complexity reductions.

Several small projects utilizing a supercomputer to solve combinatorial problems. Most recently, calculating sequential representation of numbers for small bases.

Improving high-dimensional indexing and retrieval time using space partitioning based methods such as iDistance.

I enjoy working with people and am willing to do research on nearly any project if it promises to be in good company and interesting. Several of these areas are listed with a short description of the topics I've looked at in that area. For specifics, please see the publications.

Research Groups

• ASARG. The Algorithmic Self-Assembly Research Group at UTRGV was started by Robert Schweller. This has been one of the most successful research groups on campus, and has given valuable research experience and publications to numerous students. In the past five years, the group has published over 10 publications involving more than 10 undergraduate students and 2 graduate students. Several other students also worked for the group in other aspects such as software development, etc.
  The group maintains a github with related software projects, of which I maintain and develop Tumble Tiles.
• Xtreme Algorithms. Xtreme Algorithms is a seminar hosted by Dr. Schweller and myself. Generally, we discuss self-assembly topics. The seminar ranges from formal talks by students to informal workshop days where we are trying to solve problems. All students are welcome and we tailor the seminar to those present.
• Summer Games. Beginning with a special topics course in the spring of 2017, this group is dedicated to looking at game complexities, good strategies, and a combinatorial game theory treatment of board games. Several students are involved in this research and are currently writing their first paper on the subject. There is no website for the group as they generally meet with Xtreme Algorithms.

Information for Students

I am always happy to talk to students about research. If you are looking to join one of these research groups, the best way to get involved is to come talk to me and start attending the Xtreme Algorithms seminar. This lets you get involved and see what the research process is like within the group.