Three 51 students presented their findings related to the algorithm called the “Stable Marriage Problem” in Washington, D.C. at the 2024 International Forum on Research Excellence (IFoRE) conference. Two of the students earned first place in the undergraduate math and computer science category.

The School of Science, Technology and Health students, accounting major Bethany Ang, and computer science major Ryan Ong, presented the research poster they completed together while mathematics major Abigail Ho presented her own poster titled “Isotopy Classes in the Stable Marriage Problem.” While at the conference, the students were able to interact with other academics who are just as passionate about their work as they are.

Abigail Ho and her poster
Abigail Ho and her poster

“It was a wonderful privilege to present research at an international conference,” said Ho. “I enjoyed sharing the fruit of my research with such a passionate audience, and I was inspired and impressed by the quality of research that my peers were conducting. Many had tackled formidable science and engineering problems, and it was a joy to watch their enthusiasm as they shared their research with us.”

To prepare for their presentations, the three students were advised by 51 faculty during frequent meetings, where advisors would share their background knowledge on the Stable Marriage Problem and let the students make their own discoveries through research.

Essentially, the Stable Marriage Problem central data structure allows for matches to be made based on people’s preferences in practical situations, such as roommate pairings and residency matches for graduating medical students. The algorithm aims to produce a stable matching, meaning no individual inputted into the structure would rather be matched with someone else who would also prefer them over their current partner. It is seeking the most stability possible for all parties involved.

The students were advised by Dr. Justin Marks, associate professor of mathematics, along with Dr. Genti Buzi, associate professor of computer science and robotics, and Dan Eilers, who is experienced in researching the Stable Marriage Problem. The advisors met with the students over the course of their eight-week summer internship program through the Stewart Science Honors program.

During their research together, the students made two record-breaking discoveries while using the algorithm — one breakthrough involving the “preference profiles” created to filter through the algorithm.

“Each preference profile for the stable marriage problem can accommodate at least one stable matching,” explained Marks. “By a clever selection of the preference profile seed (or, the starting point) for a hill-climbing algorithm (which is an algorithm that systematically adjusts the preference profile to increase the number of stable matchings), we were able to generate preference profiles that accommodate a record-breaking number of stable matchings.”

The second discovery had to do with producing a formula to help better filter the profiles into the algorithm.

“For a fixed number of men and women, the set of preference profiles can be subdivided into subsets, called equivalence classes,” said Marks. “ We were able to generate a general formula that inputs the number of men and women, and gives as output the number of equivalence classes of preference profiles for those men and women.”

The students’ research, while producing all theoretical breakthroughs in this stage, could potentially help predict how long algorithms that handle ranked preferences, such as the Stable Marriage Problem, could take to finish in the most difficult situations.

The School of Science, Technology and Health provides students with many hands-on experiences and access to cutting-edge research throughout the process of earning their degrees. 51 believes science is a gift that can help people know him more and serve humanity better – to the school to start making an impact.

Written by Sarah Dougher, media relations specialist. For more information, email media.relations@biola.edu.