In a social network, even about the same information the excitement between different users are different. If we want to spread a piece of new information and maximize the expected total amount of excitement, which seed users should we choose? This problem indeed is substantially different from the renowned influence maximization problem and cannot be tackled using the existing approaches. In this paper, motivated by the demand in a few interesting applications, we model the novel problem of activity maximization, and tackle the problem systematically. We first analyze the complexity and the approximability of the problem. We develop an upper bound and a lower bound that are submodular so that the Sandwich framework can be applied. We then devise a polling-based randomized algorithm that guarantees a data dependent approximation factor. Our experiments on four real data sets clearly verify the effectiveness and scalability of our method, as well as the advantage of our method against the other heuristic methods.

For a long time, PageRank has been widely used for authority computation and has been adopted as a solid baseline for evaluating social influence related applications. However, when measuring the authority of network nodes, the traditional PageRank method does not take the nodes’ prior knowledge into consideration. Also, the connection between PageRank and social influence modeling methods is not clearly established. To that end, this article provides a focused study on understanding PageRank as well as the relationship between PageRank and social influence analysis. Along this line, we first propose a linear social influence model and reveal that this model generalizes the PageRank-based authority computation by introducing some constraints. Then, we show that the authority computation by PageRank can be enhanced if exploiting more reasonable constraints (e.g., from prior knowledge). Next, to deal with the computational challenge of linear model with general constraints, we provide an upper bound for identifying nodes with top authorities. Moreover, we extend the proposed linear model for better measuring the authority of the given node sets, and we also demonstrate the way to quickly identify the top authoritative node sets. Finally, extensive experimental evaluations on four real-world networks validate the effectiveness of the proposed linear model with respect to different constraint settings. The results show that the methods with more reasonable constraints can lead to better ranking and recommendation performance. Meanwhile, the upper bounds formed by PageRank values could be used to quickly locate the nodes and node sets with the highest authorities.

Imagine we are introducing a new product through a social network, where we know for each user in the network the purchase probability curve with respect to discount. Then, what discount should we offer to those social network users so that the adoption of the product is maximized in expectation under a predefined budget? Although influence maximization has been extensively explored, surprisingly, this appealing practical problem still cannot be answered by the existing influence maximization methods. In this paper, we tackle the problem systematically. We formulate the general continuous influence maximization problem, investigate the essential properties, and develop a general coordinate descent algorithm as well as the engineering techniques for practical implementation. Our investigation does not assume any specific influence model and thus is general and principled. At the same time, using the most popularly adopted independent influence model as a concrete example, we demonstrate that more efficient methods are feasible under specific influence models. Our extensive empirical study on four benchmark real world networks with synthesized purchase probability curves clearly illustrates that continuous influence maximization can improve influence spread significantly with very moderate extra running time comparing to the classical influence maximization methods.

Given a temporal weighted graph that consists of a potentially endless stream of updates, we are interested in finding density bursting subgraphs (DBS for short), where a DBS is a subgraph that accumulates its density at the fastest speed. Online DBS detection enjoys many novel applications. At the same time, it is challenging since the time duration of a DBS can be arbitrarily long but a limited size storage can buffer only up to a certain number of updates. To tackle this problem, we observe the critical decomposability of DBSs and show that a DBS with a long time duration can be decomposed into a set of indecomposable DBSs with equal or larger burstiness. We further prove that the time duration of an indecomposable DBS is upper bounded and propose an efficient method TopkDBSOL to detect indecomposable DBSs in an online manner. Extensive experiments demonstrate the effectiveness, efficiency and scalability of TopkDBSOL in detecting significant DBSs from temporal graphs in real applications.