A Theoretical Study of Reconfigurability for Numerical Algorithms on a Reconfigurable Network

Using todays new supercomputers, programming is often a problem because of the lack of tools and libraries. Some people have tried to develop linear algebra libraries which can be easily used on a broad range of supercomputers. In the case of distributed memory multicomputers, those numerical routines are not sufficient, communication routines have to be added for the data movements, load and unload of the machine. In this poster, we show, for distributed memory multicomputers, the major interests and limitations of the communication network reconfigurability. For each of the basic operations studied, we compare one algorithm on a classical fixed topology and one algorithm issued of the reconfiguration of the network for its execution. The chosen fixed topology is the two-dimensional torus which gives good average results and thus allows to chain efficiently successive operations. If it is possible to configure the network before the execution of one routine, we try to determine the best topology. The cost of the (re-)configuration with a quasi-dynamic reconfigurable network is taken into account in our complexity analysis. It can range from one topology configuration during the whole computation to one topology reconfiguration for each computation or communication subroutine. The algorithms studied are matrix transposition, broadcast and scattering operations and their chaining with a matrix product (rank-2k updates). We tune the parameters of our analysis regarding the Inmos T800 caracteristics.