Monte Carlo Linear System Solver using MapReduce

Solving systems of linear algebraic equations (SLAE) is a problem often encountered in fields like engineering, physics, computer science and economics. As the number of unknowns in the linear system grows, the runtime and the memory requirement of solving SLAE increases dramatically. To manage this, the execution of the solver should be parallelizable and be performed in distributed environments like cloud. However, to fully take the advantage of cloud infrastructure, one should adapt the SLAE to frameworks that can successfully exploit the cloud resources like the MapReduce framework, which provides automatic parallelism, scalability and fault tolerance. With this goal, in our previous work we have adapted a SLAE algorithm Conjugate Gradient (CG) to Hadoop MapReduce framework. However, the relative complexity and the iterative structure of the CG algorithm makes it unsuited for Hadoop, which is designed for embarrassingly parallel data intensive tasks. One of the most widely used types of embarrassingly parallel algorithms are algorithms based on the Monte Carlo method. This paper presents a Monte Carlo based linear system solver that is adapted to the MapReduce model, and compares the resulting parallel efficiency and scalability to the CG implementation. The detailed analysis shows that the algorithm performs better than the Hadoop CG implementation, however loses to Twister, an alternative MapReduce implementation.