The ever-increasing demand for modern communication services and the rising cost of capital and operating expenditures have led to interest in multi-operator network collaborations. These network operators manage different network domains and infrastructures, such that their topologies may be disjointed from each other, and require the addition of intermediate interconnection links for the domains to communicate with each other. The main contribution of this paper is the proposal of an integer linear program for finding the optimum set of interconnection links to be added to the multi-domain networks such that the multi-domain networks become a connected graph, while minimizing either (1) the total length of added interconnection links, (2) the total shortest path length between all the border nodes of the multi-domain networks, or (3) the total number of shortest hop counts between all the border nodes of the multi-domain networks. The proposed integer linear program is shown to find the optimum solution under various properties for the multi-domain networks, albeit with increased computation time as the size of the problem increases. Simulation results using randomly generated multi-domain networks show a trade-off in terms of length of added links, shortest path length and shortest path hop count for each specific objective function.
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