Competitiveness Maximization on Complex Networks.

We consider a model of competition on complex networks, in which two competitors are fixed to opposite states while other agents, called normal agents, adjust their states according to a distributed consensus protocol. Suppose that one of the competitors could enhance its influence by creating new links. A natural question is, when the number of new links is limited due to the limited resource, how to add these links so as to maximize the influence of the given competitor over the other one (called competitiveness). We consider two competitiveness maximization problems: Problem 1 tries to maximize the number of supporters of the competitor, while Problem 2 tries to maximize the total supporting degree of normal agents toward the competitor. We prove that Problem 1 is NP-hard. We also show that the objective function of Problem 2 is monotonous and submodular, and hence there exists a polynomial-time greedy algorithm (GA) approximately solving Problem 2. Several centrality-based heuristic algorithms of less computational burden are also designed to provide approximate solutions to these two problems. We carry out extensive simulations to check the performances of these algorithms in six real networks. We find that GA always provides the best approximate solution to Problem 2, while for Problem 1, GA only has the best performance in directed networks. Furthermore, among those heuristic algorithms, an algorithm based on centrality in descending order is better than its counterpart in ascending order in solving Problem 2 in statistical sense. But for Problem 1, the performance of the centrality-based heuristic algorithms is more sensitive to the network structure and the locations of competitors. [ABSTRACT FROM AUTHOR]