Polynomial-time Capacity Calculation and Scheduling for Half-Duplex 1-2-1 Networks

This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this paper is the design of two polynomial-time algorithms that: (i) compute the approximate capacity of the 1-2-1 half-duplex network and, (ii) find the network schedule optimal for the approximate capacity. The paper starts by expressing the approximate capacity as a linear program with an exponential number of constraints. A core technical component consists of building a polynomial-time separation oracle for this linear program, by using algorithmic tools such as perfect matching polytopes and Gomory-Hu trees.