Sketch-based Influence Maximization and Computation

Abstract

Propagation of contagion through networks is a fundamental process. It is used to model the spread of information, influence, or a viral infection. Diffusion patterns can be specified by a probabilistic model, such as Independent Cascade (IC), or captured by a set of representative traces.Basic computational problems in the study of diffusion are influence queries (determining the potency of a specified seed set of nodes) and Influence Maximization (identifying the most influential seed set of a given size). Answering each influence query involves many edge traversals, and does not scale when there are many queries on very large graphs. The gold standard for Influence Maximization is the greedy algorithm, which iteratively adds to the seed set a node maximizing the marginal gain in influence. Greedy has a guaranteed approximation ratio of at least (1 − 1/e) and actually produces a sequence of nodes, with each prefix having approximation guarantee with respect to the same-size optimum. Since Greedy does not scale well beyond a few million edges, for larger inputs one must currently use either heuristics or alternative algorithms designed for a pre-specified small seed set size.We develop a novel sketch-based design for influence computation. Our greedy Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods. It still has a guaranteed approximation ratio, and in practice its quality nearly matches that of exact greedy. We also present influence oracles, which use linear-time preprocessing to generate a small sketch for each node, allowing the influence of any seed set to be quickly answered from the sketches of its nodes.

Outward Influence and Cascade Size Estimation in Billion-scale Networks

“…• Constant model: All the edges has the same constant probability p as in [6,8,17]. We consider three di erent values of p, i.e.…”

“…Most of the existing work in network cascades uses stochastic diffusion models and estimates the in uence spread through sampling [8,11,17,23,29,31]. The common practice is to use a xed number of samples, e.g.…”

“…The common practice is to use a xed number of samples, e.g. 10K or 20K [8,17,29,31], to estimate the expected size of the cascade, aka in uence spread. Not only is there no single sample size that works well for all networks of di erent sizes and topologies, but those approaches also do not provide any accuracy guarantees.…”

Detecting Critical Links in Complex Network to Maintain Information Flow/Reachability

“…We can quite efficiently calculate the bottom-k sketch of each node in the network by orderly assigning the rank values from the smallest one to those nodes reachable by reversely following links over the network. Based on this framework, a greedy Sketch-based Influence Maximization (SKIM) algorithm has been proposed, and it has been shown that the SKIM algorithm scales to graphs with billions of edges, with one to two orders of magnitude speedup over the best greedy methods [13]. Thus, we also develop our method of detecting critical links under the framework of the bottom-k sketching algorithm.…”

“…Here, we used the same random value r(v) assignment for each trial so that the bottom-k sketches of all the nodes are the same for any method, i.e., it is guaranteed that each method can produce the same result. Figure 1 shows the computation times of each method for five trials plotted by dots and the average values over these trials plotted by different markers as indicated in the figure, where we set k = 64 for calculation of the bottom-k sketches of all the nodes according to [13]. Figure 1(a) compares the actual processing times of these methods, where our programs implemented in C were executed on a computer system equipped with two Xeon X5690 3.47GHz CPUs and a 192GB main memory with a single thread within the memory capacity.…”