Stochastic Graph Exploration with Limited Resources

In recent years, the explosion of research on large-scale networks has been fueled to a large extent by the increasing availability of large, detailed network data sets. Specifically, exploration of social networks constitutes a growing field of research, as they generate a huge amount of data on a daily basis and are the main tool for networking, communications, and content sharing. Exploring these networks is resource-consuming (time, money, energy, etc.). Moreover, uncertainty is a crucial aspect of graph exploration since links costs are unknown in advance, e.g., creating a positive influence between two people in social networks. One approach to model this problem is the stochastic graph exploration problem [4], where, given a graph and a source vertex, rewards on vertices, and distributions for the costs of the edges. The goal is to probe a subset of the edges, so the total cost of the edges is at most some prespecified budget, and the sub-graph is connected, containing the source vertex, and maximizes the total reward of the spanned vertices. In this stochastic setting, an optimal probing strategy is likely to be adaptive, i.e., it may determine the next edge to probe based on the realized costs of the already probed edges. As computing such adaptive strategies is intractable [15], we focus on developing non-adaptive strategies, which fix a list of edges to probe in advance. A non-adaptive strategy would not be competitive versus the optimal adaptive one unless it uses a budget augmentation. The current results demand an augmentation factor, which depends logarithmically on the number of nodes. Such a factor is unrealistic in large-scale network scenarios. In this paper, we provide constant competitive non-adaptive strategies using only a constant budget augmentation for various scenarios.