Data caching in the cloud is an efficient way to improve the QoS of diverse data applications. However, this benefit is not freely available, given monetary cost to manage the caches in the cloud. In this paper, we study the data caching problem in the cloud that is driven by the monetary cost reduction, instead of the hit rate under limited capacity as in traditional cases. In particular, given a stream of requests $\mathcal{R}$ to a shared data item, we present a shortest-path based optimal algorithm that can minimize the total transfer and caching costs within O(mn) time for off-line case, here m represents the number of nodes in the network, while n is the length of the request stream. The cost model in this computation is semi-homo, which indicates that all pairs of nodes have the same transfer cost, but each cache server node has its own caching cost rate. Our off-line algorithm improves the previous results not only in reducing the time complexity from O(m2n) to O(mn), but also in relaxing the cost model to be semi-homogeneous, rendering the algorithm more practical in reality. Furthermore, we also study this problem in its online form, and by extending the anticipatory caching idea, we propose a 2-competitive online algorithm based on the same cost model and show its tightness by giving a lower bound of the competitive ratio as 2 - o(1) for any deterministic online algorithm. We provably achieve these results with our deep insights into the problem and careful analysis of the solution algorithms, together with a trace-based study to evaluate their performance in reality.