Analyzing Algebraic Curves By Cluster Computing

We describe a parallel solution to the problem of resolving non-ordinary singularities of a plane algebraic curve. The original sequential program is implemented in the software library CASA on top of the computer algebra system Maple. The new parallel version is based on Distributed Maple, a distributed programming extension written in Java. We evaluate the performance of the program in a cluster environment and compare it to that on a massively parallel multiprocessor. Keywords: Computer algebra, Maple, parallel algorithm, cluster, Java. 1. INTRODUCTION We describe a parallel solution to the problem of resolving non-ordinary singularities of a plane algebraic curve. The starting point of our work is the library CASA (computer algebra software for constructive algebraic geometry) which has been developed since 1990 by various researchers under the direction of the third author [5]. CASA is based on the computer algebra system Maple. In order to parallelize a number of CASA functions,..

Manager-Worker Parallelism versus Dataflow in a Distributed Computer Algebra System

We analyze two implementation variants of a parallel computer algebra algorithm in Distributed Maple. The original solution uses a manager-worker mechanism to control task scheduling, which requires an elaborate administration scheme. The new algorithm is based on a dataflow approach where all tasks are immediately started, automatically scheduled by the runtime system, and implicitly synchronized by task dependencies; non-determinism is effectively applied to provide more potential for parallelism. It turns out that the new version is not only more declarative (closer to the mathematical problem description) but also more efficient than the original solution

Algorithm analysis through proof complexity

Proof complexity can be a tool for studying the efficiency of algorithms. By proving a single lower bound on the length of certain proofs, we can get running time lower bounds for a wide category of algorithms. We survey the proof complexity literature that adopts this approach relative to two NP-problems: k-clique and 3-coloring