Associate Professor Nancy Ann Neudauer from Pacific University in Forest Grove, Oregon
Do you find yourself waiting for your computer to bring up a file or program? Wonder what it is doing when you hear the disk spinning? Do you tend to open the same files or applications each time you use the computer, maybe even in the same order? Using mathematics, combined with assumptions about your behaviour, we can make your computer run faster.
The time to access files on a computer can vary greatly depending on how the files are organized on the hard drive. Disk defragmenters rearrange data records, but many do this by simply gathering files in one place, considering a static system rather than addressing the dynamic optimization problem.
Problems that present themselves in industry settings often have mathematical formulations, but this is not always transparent from how they are posed. How do mathematicians tackle an open ended problem without clear parameters, equations, or assumptions? Even if we find a good statement of the problem, there are entire classes of problems we know we can't solve at all. What do you tell your boss if you realize on the first day of a project that your problem can't be solved? Sometimes companies don't care about the best solution, but are happy to have a better one.
We discuss the process of tackling the disk layout problem, including attempts to understand the computer's geometry, deciding how to measure expected access time, refining assumptions, and stating the problem as one that we recognize. Finally we consider strategies for solving the problem. And we visit some beautiful mathematics along the way