I have a different series of papers on algorithms for computational algebra
for which I will add pointers as I become more ambitious.
For pointers to me, personally,
see my home page.
(last modified, Oct. 8, 1997)
G. Cooperman, ``TOP-C: A Task-Oriented Parallel C Interface'', 5-th International Symposium on High Performance Distributed Computing (HPDC-5), IEEE Press, 1996, pp. 141--150. (N.B.: The paper on Gaussian elimination provides a good illustration of the principles of TOP-C.)
G. Cooperman, ``GAP/MPI: Facilitating Parallelism'', Proc. of DIMACS Workshop on Groups and Computation II 28, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, L. Finkelstein and W.M. Kantor (eds.), AMS, Providence, RI, 1997, pp. 69--84.
G. Cooperman, ``STAR/MPI: Binding a Parallel Library to Interactive Symbolic Algebra Systems'', Proc. of International Symposium on Symbolic and Algebraic Computation (ISSAC '95), ACM Press, pp. 126--132.
G. Cooperman and V. Greenberg, ``TOP-WEB: Task-Oriented Metacomputing on the Web'', G. Cooperman and V. Grinberg, International Journal of Parallel and Distributed Systems and Networks 1, 1998, pp.~184--192
G. Cooperman and M. Tselman, ``Using Tadpoles to Reduce Memory and Communication Requirements for Exhaustive, Breadth-First Search Using Distributed Computers'', Proc. of ACM Symposium on Parallel Architectures and Algorithms (SPAA-97), ACM Press, 1997, pp. 231--238; also N.U. Tech. Rept. NU-CCS-97-02, 1997.
G. ooperman, G. Hiß, K. Lux, and J. Müller, ``The Brauer tree of the principal 19-block of the sporadic simple Thompson group'', J. of Experimental Mathematics 6(4), 1997, pp& 293-300.
G. Cooperman, ``Practical Task-Oriented Parallelism for Gaussian Elimination in Distributed Memory'', Linear Algebra Applications 275-276, 1998, pp. 107-120.
G. Cooperman and G. Havas, ``Practical Parallel Coset Enumeration'', Proc. of Workshop on High Performance Computation and Gigabit Local Area Networks} G.& Cooperman, G.& Michler and H.& Vinck (eds.), Lecture notes in control and information sciences& 226, Springer Verlag, pp.& 15--27.
G. Cooperman, L. Finkelstein, M.& Tselman and B.& York, ``Constructing Permutation Representations for Matrix Groups'', J. of Symbolic Computation& 24, 1997, pp.& 1--18.
To date, there have been a number of notable successes in computational algebra, which provided the initial testbeds. These successes include: finding a permutation representation of Lyons's group of degree 9,606,125 (GCL/MPI, 8 SPARC-2's, 12 hours, joint with Finkelstein and Tselman, Northeastern U.); condensation of a permutation matrix representation of J_4 from dimension 173,067,389 to a matrix representation for an algebra of dimension 5,693 (GCL/MPI, 14 heavily loaded Alpha's, 2-1/2 days, joint with Tselman, Northeastern U.); and enumeration of 8,835,156 cosets in order to determine a permutation representation of Lyons's group from a presentation (TOP-C, 4-processor Convex, 6 hours, joint with Havas, U. of Queensland, Australia).
Each of these algebraic computations were the largest of their kind at that time, and in each case, almost linear speedup with the number of processors was seen. Each example has begun with a sequential algorithm and used the parallel methodology to parallelize the algorithm in a natural manner. For example, the coset enumeration used sequential code written 6-1/2 years earlier by Schönert with no thought for parallelization. Approximately 30 lines of a 1400 line C program were modified, and the program was then linked with the TOP-C library to achieve the parallelization. Each of these tests on larger problems has stressed further the general parallelization methodology and led to new ideas. Ongoing work in this spirit includes condensation of a permutation matrix representation of Th from dimension 976,841,775 to a matrix representation for an algebra of dimension 1,403 (GCL/MPI, 7 Alpha 3000's, 3 weeks expected time, joint with Lux, RWTH, Aachen, Germany and Mueller, Heidelberg, Germany) and construction of a permutation representation of dimension 173,067,389 for J_4 over GL(1333,11) (TOP-C, about 200 nodes of SP-2, under 2 days expected, joint with Michler's group) at Essen, Germany.