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In heterogeneous networks (HetNets), the load between macrocell base stations (MBSs) and small-cell base stations (SBSs) is imbalanced due to their different transmission powers and locations. This load imbalance significantly impacts system performance and affects the experience of mobile users (MUs) with different priorities. In this paper, we aim to distributively optimize the user association in HetNets with various user priorities to solve the load balancing problem. Since the user association is a binary matching problem, which is NP-hard, we propose a distributed belief propagation (BP) algorithm to approach the optimal solution. We first develop a factor graph model, using the network topology, to represent this user association problem. With this factor graph, we propose a novel distributed BP algorithm by adopting the proportional fairness as the objective. Next, we theoretically prove the existence of the fixed point in our BP algorithm. To be more practical, we develop an approximation method to significantly reduce the computational and communication complexity of the BP algorithm. Furthermore, we analyze some properties of the factor graph relevant to the performance of the BP algorithm using the stochastic geometry. Simulation results show that 1) the proposed BP algorithm well approaches the optimal system performance and achieves a much better performance compared with other association schemes and that 2) the analytical results on the average degree distribution and sparsity of the factor graph match with those obtained from the Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the problem of relay assignment in cooperative wireless networks having multiple sources, multiple relays, and a single destination. With the objective of maximizing the minimum capacity among all sources in the network, a mixed-integer linear programming (MILP) problem is formulated, which can be solved by standard branch-and-bound algorithms. To reduce computational complexity, a greedy solution in the form of a lexicographic bottleneck assignment algorithm is proposed. Simulation results obtained for the IEEE 802.16j uplink scenarios show that the greedy algorithm performs very close to the optimal solution but at a much lower computational cost. The proposed greedy solution can also be tailored to provide further improvements on other network performance criteria. [ABSTRACT FROM PUBLISHER]