Linear interference alignment (LIA) is one of the key interference mitigation techniques to enhance the wireless MIMO network capacity. The generic LIA feasibility amounts to whether or not a well-structured random matrix with entries drawn from a continuous distribution has full row-rank almost surely. Recently, a randomized algebraic test of feasibility was proposed in the literature. It is a pseudo-polynomial bounded-error probabilistic algorithm in nature, and has intrinsic limitations of requiring an inordinate amount of running time and memory even for a moderate sized input and being prone to round-off errors in floating-point computations. This paper presents necessary conditions and sufficient conditions of the generic LIA feasibility and develops fast and robust tests of them based on network flow. In certain settings, these conditions are both necessary and sufficient, and their flow-based tests yield efficient algorithm for feasibility test.
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