Structure of optimal schedules in diamond networks
We consider Gaussian diamond networks with n half-duplex relays. At any point of time, a relay can either be in a listening (L) or transmitting (T) state. The capacity of such networks can be approximated to within a constant gap (independent of channel SNRs) by solving a linear program that optimizes over the 2(n) relaying states. We recently conjectured, and proved for the cases of n = 2, 3, that there exist optimal schedules with at most n+1 active states, instead of the possible 2(n). In this paper we develop a computational proof strategy that relies on submodularity properties of information flow across cuts in the network and linear programming duality to resolve the conjecture. We implement the strategy for n = 4, 5, 6 and show that indeed there exist optimal schedules with at most n+1 active states in these cases (1).
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Record created on 2015-04-13, modified on 2016-08-09