Method maximizing the spread of influence in directed signed weighted graphs

We propose a new method for maximizing the spread of influence, based on the identification of significant factors of the total energy of a control system. The model of a socio-economic system can be represented in the form of cognitive maps that are directed signed weighted graphs with cause-and-effect relationships and cycles. Identification and selection of target factors and effective control factors of a system is carried out as a solution to the optimal control problem. The influences are determined by the solution to optimization problem of maximizing the objective function, leading to matrix symmetrization. The gear-ratio symmetrization is based on computing the similarity extent of fan-beam structures of the influence spread of vertices v_i and v_j to all other vertices. This approach provides the real computational domain and correctness of solving the optimal control problem. In addition, it does not impose requirements for graphs to be ordering relationships, to have a matrix of special type or to fulfill stability conditions. In this paper, determination of new metrics of vertices, indicating and estimating the extent and the ability to effectively control, are likewise offered. Additionally, we provide experimental results over real cognitive models in support

Beyond Worst-Case (In)approximability of Nonsubmodular Influence Maximization

We consider the problem of maximizing the spread of influence in a social network by choosing a fixed number of initial seeds, formally referred to as the influence maximization problem. It admits a $(1-1/e)$-factor approximation algorithm if the influence function is submodular. Otherwise, in the worst case, the problem is NP-hard to approximate to within a factor of $N^{1-\varepsilon}$. This paper studies whether this worst-case hardness result can be circumvented by making assumptions about either the underlying network topology or the cascade model. All of our assumptions are motivated by many real life social network cascades. First, we present strong inapproximability results for a very restricted class of networks called the (stochastic) hierarchical blockmodel, a special case of the well-studied (stochastic) blockmodel in which relationships between blocks admit a tree structure. We also provide a dynamic-program based polynomial time algorithm which optimally computes a directed variant of the influence maximization problem on hierarchical blockmodel networks. Our algorithm indicates that the inapproximability result is due to the bidirectionality of influence between agent-blocks. Second, we present strong inapproximability results for a class of influence functions that are "almost" submodular, called 2-quasi-submodular. Our inapproximability results hold even for any 2-quasi-submodular $f$ fixed in advance. This result also indicates that the "threshold" between submodularity and nonsubmodularity is sharp, regarding the approximability of influence maximization.Comment: 53 pages, 20 figures; Conference short version - WINE 2017: The 13th Conference on Web and Internet Economics; Journal full version - ACM: Transactions on Computation Theory, 201

Seeds Buffering for Information Spreading Processes

Seeding strategies for influence maximization in social networks have been studied for more than a decade. They have mainly relied on the activation of all resources (seeds) simultaneously in the beginning; yet, it has been shown that sequential seeding strategies are commonly better. This research focuses on studying sequential seeding with buffering, which is an extension to basic sequential seeding concept. The proposed method avoids choosing nodes that will be activated through the natural diffusion process, which is leading to better use of the budget for activating seed nodes in the social influence process. This approach was compared with sequential seeding without buffering and single stage seeding. The results on both real and artificial social networks confirm that the buffer-based consecutive seeding is a good trade-off between the final coverage and the time to reach it. It performs significantly better than its rivals for a fixed budget. The gain is obtained by dynamic rankings and the ability to detect network areas with nodes that are not yet activated and have high potential of activating their neighbours.Comment: Jankowski, J., Br\'odka, P., Michalski, R., & Kazienko, P. (2017, September). Seeds Buffering for Information Spreading Processes. In International Conference on Social Informatics (pp. 628-641). Springe

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Probing Limits of Information Spread with Sequential Seeding

We consider here information spread which propagates with certain probability from nodes just activated to their not yet activated neighbors. Diffusion cascades can be triggered by activation of even a small set of nodes. Such activation is commonly performed in a single stage. A novel approach based on sequential seeding is analyzed here resulting in three fundamental contributions. First, we propose a coordinated execution of randomized choices to enable precise comparison of different algorithms in general. We apply it here when the newly activated nodes at each stage of spreading attempt to activate their neighbors. Then, we present a formal proof that sequential seeding delivers at least as large coverage as the single stage seeding does. Moreover, we also show that, under modest assumptions, sequential seeding achieves coverage provably better than the single stage based approach using the same number of seeds and node ranking. Finally, we present experimental results showing how single stage and sequential approaches on directed and undirected graphs compare to the well-known greedy approach to provide the objective measure of the sequential seeding benefits. Surprisingly, applying sequential seeding to a simple degree-based selection leads to higher coverage than achieved by the computationally expensive greedy approach currently considered to be the best heuristic