  The problem of exact repair of a failed node in multi-hop networked
distributed storage systems is considered. Contrary to the most of the current
studies which model the repair process by the direct links from surviving nodes
to the new node, the repair is modeled by considering the multi-hop network
structure, and taking into account that there might not exist direct links from
all the surviving nodes to the new node. In the repair problem of these
systems, surviving nodes may cooperate to transmit the repair traffic to the
new node. In this setting, we define the total number of packets transmitted
between nodes as repair-cost. A lower bound of the repaircost can thus be found
by cut-set bound analysis. In this paper, we show that the lower bound of the
repair-cost is achievable for the exact repair of MDS codes in tandem and grid
networks, thus resulting in the minimum-cost exact MDS codes. Further, two
suboptimal (achievable) bounds for the large scale grid networks are proposed.
