We describe the design and implementation of the Distributed Threads System (DTS), a programming environment for the parallelization of irregular and highly data-dependent algorithms. DTS extends the support for fork/join parallel programming from shared memory threads to a distributed memory environment. It is currently implemented on top of PVM, adding an asynchronous RPC abstraction and turning the net into a pool of anonymous compute servers. Each node of DTS is multithreaded using the C threads interface and is thus ready to run on a multiprocessor workstation. We give performance results for a parallel implementation of the RSA cryptosystem, parallel long integer multiplication, and parallel multi-variate polynomial resultant computation.

We describe the Distributed Object-Oriented Threads System (DOTS), a programming environment designed to support object-oriented fork/join parallel programming in a heterogeneous distributed environment. A mixed network of Windows NT PC’s and UNIX workstations is transformed by DOTS into a homogeneous pool of anonymous compute servers forming together a multicomputer. DOTS is a complete redesign of the Distributed Threads System (DTS) using the object-oriented paradigm both in its internal implementation and in the programming paradigm it supports. It has been used for the parallelization of applications in the field of computer algebra and in the field of computer graphics. We also give a brief account of applications in the domain of symbolic computation that were developed using DTS. Key words: distributed threads system, heterogeneous networks, Windows NT

Abstract not found

The Gröbner Walk is an algorithm that converts a given Gröbner basis of a polynomial ideal I of arbitrary dimension to a Gröbner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Gröbner fan of I. We report on our experiences with an implementation of the walk. We discuss several algorithmic variations as well as important implementation techniques whose combined effect is to elevate the walk to a new level of performance.

The Grobner Walk is an algorithm which converts a given Grobner basis of a polynomial ideal I of arbitrary dimension to a Grobner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Grobner fan of I . We report on our experiences with a first implementation of the walk connected with a state-of-the-art Grobner basis package. Our implementation allows us to evaluate the walk on a large set of non-trivial examples. We can thus give an estimation when it is promising to apply the walk for the computation of lexicographic Grobner Bases. 1 Introduction It is well known that the form and size of a Grobner basis of a polynomial ideal [2] depends heavily on the underlying term order, and that the same is true for the complexity of its computation. Unfortunately, the lexicographic term orders needed for polynomial system solving are particularly bad in this respect. A possible strategy to overcome this difficulty is to comp...

We report on the development of PARSAC-2, a library of parallel algebraic algorithms designed specifically for networks of multiprocessor workstations. PARSAC-2 is built upon the S-threads system environment for multi-threaded symbolic computation. S-threads provides virtual parallelism by mapping thousands of very light-weight processes onto the processors of a workstation. It is currently being extended with network functionality, so that heavy-weight processes can be mapped across the network while preserving the S-threads interface. The current goal of algorithm development in PARSAC is the construction of a parallel polynomial equation solver using Groebner-Bases. We report on the design of a strategycompliant parallel Groebner-Basis computation with factorization. Introduction Symbolic computation is a high-level computational task which makes it comparatively complex and slow. However, it is increasingly applied in science and engineering [FGHK94] and any significant increase i...