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Table 5 Complexity comparison

From: Joint user clustering and resource allocation for device-to-device communication underlaying MU-MIMO cellular networks

Schemes IA optimal IA two-step IA random Location-based
Complexity of the throughput calculation \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}M \) \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}M \) K rb M K rb M
Complexity of the search \( \left({\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}\right)\hat{\mkern6mu} {K}_{rb} \) \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d} \) K rb K rb
Schemes Orthogonal optimal Orthogonal two-step Orthogonal random
Complexity of the throughput calculation \( \left({K}_{rb,c}{\mathrm{C}}_{K_c}^{N_c}+{K}_{rb,d}{K}_d\right)M \) \( \left({K}_{rb,c}{\mathrm{C}}_{K_c}^{N_c}+{K}_{rb,d}{K}_d\right)M \) K rb M
Complexity of the search \( {K}_d\hat{\mkern6mu} {K}_{rb,d}+{C}_{K_c}^{N_c}\hat{\mkern6mu} {K}_{rb,c} \) \( {K}_d{K}_{rb,d}+{\mathrm{C}}_{K_c}^{N_c}{K}_{rb,c} \) K rb
Schemes Multiplex optimal Multiplex two-step Multiplex random
Complexity of the throughput calculation \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}M \) \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}M \) K rb M
Complexity of the search \( \left({\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d}\right)\hat{\mkern6mu} {K}_{rb} \) \( {K}_{rb}{\mathrm{C}}_{K_c}^{N_c}{\mathrm{C}}_{K_d}^{N_d} \) K rb