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Dynamic Web contents are generated by running application programs on base data which often change frequently. Geographically replicating the applications that construct these contents (including the programs and the related data they access) is an effective approach to improve their access latency. To maintain the freshness of an object replica, the new version of the object either has to be fetched from remote servers or be reconstructed locally when the origin copy is updated. We present a theoretical study on geographical replication of dynamic Web contents with the objective of minimizing the consistency management costs in terms of update transfers and object reconstruction. The dependencies among dynamic objects and base data are modeled as a directed acyclic graph. We formulate the minimum cost replication problem under a flat framework of update delivery. The problem is solved by first transforming it into a minimum cut problem in a flow network. A polynomial-time algorithm is then proposed to compute the optimal replication strategy which designates where each object should be replicated and how to keep the replicas up-to-date.