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In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous and efficient protocol should be used to repair the failed node. The repair process causes traffic and consequently transmission cost in the network. Recent results found the optimal traffic storage tradeoff, and proposed regenerating codes to achieve the optimality. The authors aim at minimizing the transmission cost in the repair process. They consider the network topology in the repair, and accordingly modify information flow graphs. Then they analyze the cut requirement and based on the results, they formulate the minimum-cost as a linear programming problem for linear costs.
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