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The performance of mobile edge computing (MEC) depends critically on thequality of the wireless channels. From this viewpoint, the recently advocatedintelligent reflecting surface (IRS) technique that can proactively reconfigurewireless channels is anticipated to bring unprecedented performance gain toMEC. In this paper, the problem of network throughput optimization of anIRS-assisted multi-hop MEC network is investigated, in which the phase-shiftsof the IRS and the resource allocation of the relays need to be jointlyoptimized. However, due to the coupling among the transmission links ofdifferent hops caused by the utilization of the IRS and the complicatedmulti-hop network topology, it is difficult to solve the considered problem bydirectly applying existing optimization techniques. Fortunately, by exploitingthe underlying structure of the network topology and spectral graph theory, itis shown that the network throughput can be well approximated by the secondsmallest eigenvalue of the network Laplacian matrix. This key finding allows usto develop an effective iterative algorithm for solving the considered problem.Numerical simulations are performed to corroborate the effectiveness of theproposed scheme.

Spectral Graph Theory Based Resource Allocation for IRS-Assisted Multi-Hop Edge Computing