A physicist has developed an algorithm that can make cancer treatments safer as well as boost Wi-Fi security, the New Scientist reports.
Carolyn Phillips, a physicist at the University of Michigan in Ann Harbor, and her colleagues have studied what they call the "filling" problem, which essentially is a mathematical version of coloring in a shape using different sized blots of paint.
Mathematicians have long studied the packing problem, which involves finding the best way to fit a set of shapes inside of a larger object. Then there is the covering problem, where smaller shapes completely cover a larger shape.
Phillips started investigating the filling problem when she was trying to model the behavior of a type of a nano-particle. "Physicists are used to thinking about simple hard objects that can't overlap, while problems of covering have been traditionally more the domain for mathematicians," she said. "Now there are nanoscale structures that can be modeled as overlapping spheres."
Phillips and her team began their study by finding the target object's "topological skeleton," which is a representation of the object being filled as a series of lines running through its center. The topological skeleton of a triangle compromises three lines that meet at a triple branching point. More complicated shapes can have several of these branching points.
The team then placed the center of the first circle at one of the branching points in the skeleton, trying to fill in as large of an area as possible. Next, subsequent smaller circles sit at the other points along the skeleton until the entire shape is filled.
The team is looking for a solution to the problem in three or more dimensions. "The skeleton of a 3D shape is more complicated," Phillips said. "Conceptually, the solutions are similar, but designing an algorithm that can actually find a good optimal solution is considerably more challenging."
However abstract Phillips' work might sound, figuring out how to fill a space using the minimum number of circles could have real world applications. She says that her technique could help radiologists use the minimum number of variously sized radiation beams to treat all areas of a tumor. It could also help design an office Wi-Fi network that would use the smallest possible antennas to ensure that the signal does not extend beyond the walls of a building. This would eliminate the need for a password on your Wi-Fi.