Parallelizing Under-Determined Inverse Problems for Network Applications

In this paper, we introduce a new technique for partitioning a large-scale under-determined linear inverse problem into multiple smaller subproblems that can be efficiently solved independently, and in parallel. When it is impossible or inefficient to solve a large-scale under-determined linear inverse problem, this technique can be used to significantly speed up the computation process without compromising the accuracy of the solution. We present numerical results that show the effectiveness of this approach when applied to network inference problems including traffic matrix estimation and network anomaly detection, both are important for managing large, complex networks and cyber security. Our proposed framework is applicable to other emerging applications in computational intelligence that can be formulated as under-determined linear inverse problems.