Professor Buss works in the field of computational complexity, which considers the fundamental nature and limitations of computation. Computational complexity treats computation in mathematical terms; rather than using computers to do mathematical calculations, it uses mathematical analysis to understand computation. In the long term, a better understanding of the fundamental properties of computation leads to better use of existing computers and better design of new ones.
Some computational problems require too much time to be feasible. Ideally, the computation time should be roughly proportional to the amount of input data that must be used in the calculation. In some cases, however, no possible computation can obtain the answer for the given data so quickly. While the precise boundary between feasible and infeasible problems depends on the particular computer in use, some problems can be shown to be infeasible for any envisionable computer.
One focus of Professor Buss's work is to characterize what properties of a problem make it amenable to solution and what properties make a problem impossible to solve quickly. These characterizations include (1) costly searches that can be avoided, (2) independence of parts, so that the solution can be computed in parallel, and (3) alternative formulations that are more amenable to solution.
In addition to abstract work, Professor Buss has applied techniques of computational complexity to problems from parallel processing (minimizing the impact of processor failures), scientific computing (mesh generation), and the solution of algebraic equations.
Degrees and awards
BSc (California Institute of Technology), PhD (Massachusetts Institute of Technology)
Industrial and sabbatical experience
Professor Buss joined the University of Waterloo upon completing his graduate studies. During his tenure, he has spent sabbaticals at the University of Massachusetts (Amherst) and the University of Washington. He has presented his work in conferences in the local geographic area, such as Toronto and Ithaca, NY (Cornell University), and around the world, from Crete to New Zealand.
J.F. Buss and K.W. Regan. Simultaneous Bounds on Time and Space. In preparation (approx. 13 pp.), 2008.
J.F. Buss and T. Islam. Guest Column: The Complexity of Fixed-Parameter Problems. Complexity Theory Guest Column 58, SIGACT News, 12 pp., 2008.
J.F. Buss and T. Islam. The Fixed-Parameter Complexity of Precedence-Constrained Multiprocessor Scheduling and PDA-Intersection Problems, In preparation (approx. 48 pp.), 2008.
J.F. Buss and T. Islam. Algorithms in the W-Hierarchy. Theory of Computer Systems, 41:445-457, 2007.
J.F. Buss and T. Islam. Simplifying the Weft Hierarchy. Theoretical Computer Science, 351:303-313, 2006.
T. Biedl, J.F. Buss, E.D. Demaine, M.L. Demaine, M. Hajiaghayi, and T. Vinar. Palindrome Recognition Using a Multidimensional Tape. Theoretical Computer Science, 302:475-480, 2003.