Multiplex Influence Maximization in Online Social Networks With Heterogeneous Diffusion Models

Abstract

Motivated by online social networks that are linked together through overlapping users, we study the influence maximization problem on a multiplex, with each layer endowed with its own model of influence diffusion. This problem is a novel version of the influence maximization problem that necessitates new analysis incorporating the type of propagation on each layer of the multiplex. We identify a new property, generalized deterministic submodular, which when satisfied by the propagation in each layer, ensures that the propagation on the multiplex overall is submodular -for this case, we formulate ISF, the greedy algorithm with approximation ratio (1 − 1/e). Since the size of a multiplex comprising multiple OSNs may encompass billions of users, we formulate an algorithm KSN that runs on each layer of the multiplex in parallel. KSN takes an α-approximation algorithm A for the influence maximization problem on a single network as input, and has approximation ratio (1− )α (o+1)k for arbitrary > 0, o is the number of overlapping users, and k is the number of layers in the multiplex. Experiments on real and synthesized multiplexes validate the efficacy of the proposed algorithms for the problem of influence maximization in the heterogeneous multiplex. Implementations of ISF and KSN are available at

A branch‐and‐cut approach for the least cost influence problem on social networks

“…There are several potential directions for future work. Allowing competition and a defender-attacker setup in the problem (see [14]) and considering influence propagation over multiple social networks (see [16]) are among such directions. Although the TU formulation in Günneç et al [12] provides a nice building block for developing an efficient approach on arbitrary graphs, it introduces a large number of variables by characterizing the incoming influence into several types.…”

“…While it can be applied to larger problems, the price-cut-and-branch is a heuristic that is not guaranteed to solve the problem to optimality (the dual bounds obtained after the root node are not valid since the branching phase does not allow for the addition of columns in this approach; i.e., only the lower bound obtained at the root node is valid). In this more general setting, they are only able to apply their approach to simulated graph instances with up to 100 nodes with an average degree up to 16. Their approach finds optimal solutions when the average degree is 4, but the quality of the solutions rapidly deteriorates when the average degree increases.…”

“…Constraint set (14) guarantees that there is at most one incoming arc with type L. Constraint set (15) ensures that an arc can be characterized with only one type of influence (H, L, or Z) and matches direction with that of the binary y variables. Constraint sets (16) and (17) are identical to the ARC model. Notice that when the underlying graph is a tree, constraint set (16) becomes redundant because constraint set (17) rules out all cycles with two arcs and there are no cycles with three or more arcs when the underlying graph is a tree.…”

“…Then, based on this information, we can apply HLZ formulation to the LCIP on DAGs. Notice that constraint sets (16) and (17) in HLZ become redundant because the influence propagation is known and is a DAG. Also, we do not need y variables any more.…”

“…In this section, we develop a branch-and-cut approach based on HLZ for solving the LCIP. To solve the LP relaxation of HLZ, it is necessary to solve the separation problem for the exponential size set of k-dicycle inequalities (16). Grötschel et al [10] present a separation procedure for k-dicycle inequalities (in the context of the linear ordering problem) which is based on the shortest path algorithm.…”