Graph-Theoretic Approach for Increasing Participation in Networks With Assorted Resources

In many cooperative networks, individuals participate actively as long as they recognize a sufficient value in participation, which depends not only on the number, but also on the attributes of other participating members. In this paper, we present a generalized model of individuals’ participation in such networks, and a strategy to maximize the number of participating individuals. Unlike most of the existing literature, our model incorporates both the network structure and the heterogeneity of individuals in terms of their attributes and resources. We consider that each individual possesses a subset of available resources (attributes), which it shares with neighbors as long as neighbors reciprocate and provide the missing resources to the individual. However, individual leaves the network if it cannot find all the resources in its neighborhood. To model this phenomenon, we introduce a graph-theoretic notion of the $(r,s)$-core, which is the sub-network consisting of only those individuals who can access all the resources by collaborating with their neighbors. Since disengagement of an individual could initiate a cascading withdrawal of more individuals from the network, one of our main goals is to prevent this unraveling and maximize the number of participating individuals. For this purpose, we utilize the notion of anchors—individuals that continue to participate (due to incentives) even if they cannot find all of the resources in their neighborhood. By introducing only a few anchors, we can significantly increase the number of participating individuals, which in our model corresponds to increasing the size of the $(r,s)$-core. We formulate and thoroughly analyze the anchors’ selection problem by classifying the cases in which the problem is polynomial-time solvable, NP-complete, and inapproximable. Further, we provide greedy and metaheuristic search algorithms to compute a set of anchors and evaluate our results on various networks. Our results are applicable to a large number of cooperative networking applications, including participatory sensing in which users develop an elaborate knowledge of their environment through sharing measurements.