May 21st, 2014
We could improve the bounds of numerical steps needed to find an exact solution for polynomial systems by multiple orders of magnitude. Given present knowledge, they are nearly optimal.
Jasmin Christian Blanchette
Thomas Lengauer (Director)
Kurt Mehlhorn (Director)
Bernt Schiele (Director)
Hans-Peter Seidel (Director)
Gerhard Weikum (Director)
While the acceleration of hardware has been a landmark of progress in computing technology in the past few decades, the computing enhancements that it provides is dwarfed by the increase in speed, performance, and robustness resulting from new algorithms.
As a point in case, the status of hardware and algorithms in 1970 allowed to compute an optimal tour of a traveling salesman (a classical optimization problem and accepted benchmark for computing power) through 120 cities. Increasing the number of cities from n to n+1 leads to a multiplicative increase of the number of possible tours by a factor of n. Thus, relying only on the increase of hardware speed, with today’s technology, and the algorithms of 1970 we could find optimal tours among only 135 cities. It is the progress in algorithms that, today, enables us to find optimal tours between many thousand of cities. Relying only on progress in hardware this performance would not be achievable in hundreds of years.
The Max-Planck Institute for Informatics is devoted to cutting-edge research in informatics with a focus on algorithms and their applications in a broad sense.