Structure of optimal schedules in diamond networks

Information Theory(2014)

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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 2n 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 2n. 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.
Gaussian processes,duality (mathematics),linear programming,relay networks (telecommunication),scheduling,Gaussian diamond networks,computational proof strategy,half-duplex relays,information flow,linear programming duality,listening state,optimal schedule structure,submodularity properties,transmitting state
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