We consider the scenario where a sender periodically sends a batch of data to a receiver over a multi-hop network, possibly using multiple paths. Our objective is to minimize peak/average Age-of-Information (AoI) subject to throughput requirements. The consideration of batch generation and multi-path communication differentiates our AoI study from existing ones. We first show that our AoI minimization problems are NP-hard, but only in the weak sense, as we develop an optimal algorithm with a pseudo-polynomial time complexity. We then prove that minimizing AoI and minimizing maximum delay are roughly equivalent, in the sense that any optimal solution of the latter is an approximate solution of the former with bounded optimality loss. We leverage this understanding to design a general approximation framework for our problems. It can build upon any $alpha$-approximation algorithm of the maximum delay minimization problem, to construct an $(alpha+c)$-approximate solution for minimizing AoI. Here $c$ is a constant depending on the throughput requirements. Simulations over various network topologies validate the effectiveness of our approach.
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