Half-Duplex Routing is NP-hard

TL;DR

This paper investigates the complexity of finding optimal half-duplex routes in relay networks, proving NP-hardness in general but offering polynomial solutions under certain network conditions.

Contribution

It establishes the NP-hardness of the half-duplex routing problem and identifies conditions for polynomial-time algorithms to find optimal routes.

Findings

NP-hardness of general half-duplex routing

Polynomial-time algorithm exists when network cycles are polynomial in number

Half-duplex capacity is half of the harmonic mean of consecutive link capacities

Abstract

Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest Full-Duplex (FD) capacity, which is given by the minimum among the point-to-point link capacities in the path. Such an approach may be suboptimal if then the nodes in the selected path are operated in Half-Duplex (HD) mode. Recently, the capacity (up to a constant gap that only depends on the number of nodes in the path) of an HD line network i.e., a path) has been shown to be equal to half of the minimum of the harmonic means of the capacities of two consecutive links in the path. This paper asks the questions of whether it is possible to design a polynomial-time algorithm that efficiently finds the path with the largest HD capacity in a relay network. This problem of finding that path is shown to be NP-hard in general. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-time algorithm can indeed be designed.