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| Mathematical technique | Merits | Demerits |
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| Coalitional game | Cooperation in this game can offer better network performance
The users are capable of making contracts which are mutually beneficial | Increase in complexity in large-scale communication networks |
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| Stackelberg game | Utility maximization for leaders and best responses for the followers are guaranteed | Need accurate channel state information between the leaders and the followers |
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| One-to-one matching | Can be used to characterize interactions between heterogeneous network nodes or devices with different objectives and information
Has capability of defining user preferences in a heterogeneous network and UEs QoS in wireless networks
The match theoretic algorithms’ solutions converge to a stable state
Match theoretic algorithms can be implemented efficiently with a self-organizing feature | It provides multiple stable points which need proper selection of appropriate matching
Optimality of a stable solution cannot be guaranteed
Dynamic algorithms require additional signaling for exchange of proposals in wireless networks. |
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| Lagrangian dual decomposition and Karush–Kuhn–Tucker conditions | Gradient-based nonlinear optimization techniques have relatively low-computational and set up time | High-dimensional and multimodal problems require infinite running time
Global optimality is not guaranteed
The continuity and differentiability assumption for the objective function does not hold for practical network systems |
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| Iterative water filling | Operations performed by this algorithm includes only basic arithmetic in addition to the logarithm function which can be implemented as a look up table | Increased complexity for multicell, multiuser, and multiantenna networks |
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| Genetic algorithm | Random mutation offers a wide range of solutions
It has a large and wide solution searching space capability
Has potential of solving multiobjective optimization problems
Use of the fitness function for evaluation offers the capability of extending to continuous and discrete optimization problems | Difficult to develop good heuristic which reflects what the algorithm has carried out
Difficult to choose parameters such as number of generations and population size
Extremely difficult to fine tune to get enhancement in performance |
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| Particle swarm optimization | It has guidelines for selecting the optimization parameters
Has variants for real, integer, and binary domains
Provides best solutions due to the capability of escaping from the local optima
Converges rapidly | Weak local search ability
It has premature convergence |
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| Graph colouring | Has suitable tools for modelling and analyzing wireless networks
Low-computational complexity for D2D networks
Provides a common formalism for different wireless network problems | Difficult in modelling the user interactions for densified (large scale) networks |
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