Dense constellations of Low Earth Orbit (LEO) small satellites are envisioned to make extensive use of the inter-satellite link (ISL). Within the same orbital plane, the inter-satellite distances are preserved and the links are rather stable. In contrast, the relative motion between planes makes the inter-plane ISL challenging. In a dense set-up, each spacecraft has several satellites in its coverage volume, but the time duration of each of these links is small and the maximum number of active connections is limited by the hardware. We analyze the matching problem of connecting satellites using the inter-plane ISL for unicast transmissions. We present and evaluate the performance of two solutions to the matching problem with any number of orbital planes and up to two transceivers: a heuristic solution with the aim of minimizing the total cost; and a Markovian solution to maintain the on-going connections as long as possible. The Markovian algorithm reduces the time needed to solve the matching up to 1000x and 10x with respect to the optimal solution and to the heuristic solution, respectively, without compromising the total cost. Our model includes power adaptation and optimizes the network energy consumption as the exemplary cost in the evaluations, but any other QoS-oriented KPI can be used instead.
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