In this paper, we investigate allocation of data partitions in the network for data objects that are partitioned by using secret sharing schemes [12] or erasure coding schemes [11]. We defined the problem as finding M nodes in the network to host the data partitions so that the total cost of reading K partitions and updating M partitions by all nodes in the network is minimized. This problem is NPhard. We proposed a SOFM-like algorithm and a heuristic algorithm for this problem. The numerical study shows both algorithms are effective for this problem. Key Words: Security, data partitioning, secret sharing, erasure coding, SOFM like Algorithm.