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Rounding Markov Chains and Iterative Load-Balancing Schemes

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Iterative Load-Balancing Schemes allow nodes to balance its load with their neighbors in each iteration. Under the assumption that load can be divided arbitrarily often (continuous case), it is well-known that such schemes correspond to Markov chains whose convergence is characterised by the spectral gap of the transition matrix. In this talk we focus on the discrete case where load is integral. We show that by employing randomised rounding, the system converges to a state where all nodes have the same load up to an additive constant within the same number of steps that are needed in the continuous case.

This talk is part of the Probability series.

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