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In this paper, we present a graph-theoretic framework for provisioning overlay network based multimedia distribution services to a diverse set of receivers. Considering resource limitations and exploiting geographical positions, it greedily constructs degree-constrained minimum-cost connected graph to manipulate the topology to a significant extent by selecting mesh neighbors and changing the metrics. Data delivery paths and forwarding nodes are chosen using the dominating set. The minimal cardinality of the dominating set reduces the system's dependency on end-hosts. Simulation is used to demonstrate that the framework is more robust and responsive to tree partitions and suitable for multi-source multimedia applications.