Understanding diffusion processes in networks has emerged as an important research topic because of its wide range of applications. Analysis of diffusion traces can help us answer important questions such as the source(s) of diffusion and the role of each node during the diffusion process. However, in large-scale networks, due to the cost and privacy concerns, it is almost impossible to monitor the entire network and collect the complete diffusion trace. In this paper, we tackle the problem of reconstructing the diffusion history from a partial observation. We formulate the diffusion history reconstruction problem as a maximum a posteriori (MAP) problem and prove the problem is NP-hard. Then, we propose a step-by-step reconstruction algorithm, which can always produce a diffusion history that is consistent with the partial observation. Our experimental results based on synthetic and real networks show that the algorithm significantly outperforms some existing methods.

This paper studies the problem of robustifying an interdependent network by rewiring a small number of links in realtime during a cascading attack. Interdependent networks have been widely used to model interconnected complex systems such as a critical infrastructure network including both the power grid and the Internet. Realtime robustification of interdependent networks, therefore, has significant practical importance. This paper formulates the problem using the Markov decision process (MDP) framework. We first show the problem is NP-hard and then develop an effective and efficient greedy algorithm, named REALWIRE, to robustify the network in realtime. REALWIREscores each link (and each node) based on the expected number of links failures resulted from the failure of the link (or the node), and rewires the links greedily according to the scores. Extensive experimental results show that REALWIREoutperforms other algorithms on multiple trobustness metrics.

This paper studies the problem of locating multiple diffusion sources in networks with partial observations. We propose a new source localization algorithm, named Optimal-Jordan-Cover (OJC). The algorithm first extracts a subgraph using a candidate selection algorithm that selects source candidates based on the number of observed infected nodes in their neighborhoods. Then, in the extracted subgraph, OJC finds a set of nodes that "cover" all observed infected nodes with the minimum radius. The set of nodes is called the Jordan cover, and is regarded as the set of diffusion sources. Considering the heterogeneous susceptible-infected-recovered (SIR) diffusion in the Erdos-Renyi (ER) random graph, we prove that OJC can locate all sources with probability one asymptotically with partial observations. OJC is a polynomial-time algorithm in terms of network size. However, the computational complexity increases exponentially in m; the number of sources. We further propose a low-complexity heuristic based on the K-Means for approximating the Jordan cover, named Approximate-Jordan-Cover (AJC). Simulations on random graphs and real networks demonstrate that both AJC and OJC significantly outperform other heuristic algorithms.

Diffusion processes in networks can be used to model many real-world processes. Analysis of diffusion traces can help us answer important questions such as the source of diffusion and the role of each node in the diffusion process. However, in large-scale networks, it is very expensive if not impossible to monitor the entire network to collect the complete diffusion trace. This paper considers diffusion history reconstruction from a partial observation and develops a greedy, step-by-step reconstruction algorithm. It is proved that the algorithm always produces a diffusion history that is consistent with the partial observation. Our experimental results based on real networks and real diffusion data show that the algorithm significantly outperforms some existing methods.