


Joshua Brakensiek
$10,000 Scholarship Recipient
Age: 17 Phoenix, AZ Category: Mathematics Project Title: “Bounds on the Size of Sound Monotone Switching Networks Accepting Permutation Sets of Directed Trees”______ _______ ________ ____ _______ 


Joshua investigated an extension of the STconnectivity problem in graph theory. The STconnectivity problem asks whether two locations in a graph have an unbroken connection between them. Joshua’s work estimated the required memory usage when the graph has a predefined structure. Instead of using a traditional model of computation (e.g. the RAM model), his research studied the memory usage under the monotone switching network model of computation.
In the main result, if the graph under consideration is known to be either not connected or equivalent to a graph without loops (i.e. a tree), then the optimal memory usage was approximated with an order of magnitude of precision greater than any previous result. Joshua’s work improves the current intuition about the monotone switching network model and may lead to deeper insights which solve a broader class of problems. His research has potential applications in medicine, epidemiology, economics, and other fields which require complex data analysis. Furthermore, Joshua’s research has connections to the longstanding L vs. NL problem, a sister problem of the P vs. NP problem, which is one of the most famous open questions in mathematics.
Joshua is a rising homeschooled senior. In college, he hopes to double major in mathematics and computer science and earn a Ph. D. in a similar field. Joshua is a 2013 gold medalist in the International Olympiad in Informatics and a USA Mathematical Olympiad Honorable Mention. He participated in the Research Science Institute in 2012.
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