Special Session on High-Performance Computer Algebra

 

Title:    Parallel Disk-Based Computation and Computational Group Theory

Eric Robinson, Gene Cooperman, Daniel Kunkle and Jürgen Müller
College of Computer Science, Northeastern University, USA

The authors have worked together over five years to develop a general methodology for parallel disk based computation. This includes: construction of a permutation representation for Thompson's group, acting on 143,127,000 points; construction of a permutation representation for the Baby Monster group (second largest of the sporadic simple groups), acting on 13,571,955,000 points; and a condensation computation for Fi_23 acting on 11,739,046,176 points that resolves an open problem in the Modular Atlas Project. At heart, these problems are search problems. The work typically required a multi-threaded, distributed program using the 30 nodes and corresponding local disks in parallel. Aggregate disk space used ranged as high as 8 terabytes. The need for the highest efficiency led to the discovery of one new search method, and the re-discovery of several other search methods. This is summarized in a taxonomy of parallel disk-based search algorithms. In addition, a new, open source package is presented that automates the difficult task of developing such parallel disk-based software. Lessons learned about the difficulties of such large computations are also presented.