Importance Sketching of Influence Dynamics in Billion-Scale Networks

Abstract

Abstract-The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious challenges in computational efficiency and scalability.In this paper, we propose a new hyper-graph sketching framework for influence dynamics in networks. The central of our sketching framework, called SKIS, is an efficient importance sampling algorithm that returns only non-singular reverse cascades in the network. Comparing to previously developed sketches like RIS and SKIM, our sketch significantly enhances estimation quality while substantially reducing processing time and memory-footprint. Further, we present general strategies of using SKIS to enhance existing algorithms for influence estimation and influence maximization which are motivated by practical applications like viral marketing. Using SKIS, we design high-quality influence oracle for seed sets with average estimation error up to 10x times smaller than those using RIS and 6x times smaller than SKIMs. In addition, our influence maximization using SKIS substantially improves the quality of solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x memory reduction for the fastest RIS-based DSSA algorithm, while maintaining the same theoretical guarantees.

The Solution Distribution of Influence Maximization: A High-level Experimental Study on Three Algorithmic Approaches

“…Since an influence estimator is randomized, each algorithm run generates random solutions as well. Despite this nature, most of the previous studies conducted few-trials experiments only, e.g., the number of trials is 3 in [70], 5 in [69], 10 in [13,15,47], 20 in [30], 50 in [16], and not explicitly stated in [14,17,19,24,26,27,31,38,39,56,57,[60][61][62]; conclusions based on them would be questionable. In this paper, we analyze the empirical distribution of random solutions made from 1,000 trials to gain a deeper understanding of the stochastic behavior of randomized algorithms.…”

“…Unlike the case of Oneshot and Snapshot, most of the research on RIS focus on a proper selection of sample number θ , or equivalently, a stopping condition for RR-set generation. The standard requirement is to draw as few RR sets as possible that yield a "theoretical worst-case guarantee" on a (1 − 1/e − ϵ)-approximation with probability 1 − δ [7,30,56,57,60,61,[68][69][70].…”

Location-Based Seeds Selection for Influence Blocking Maximization in Social Networks

“…The main idea of RIS is not to estimate the influence from seed nodes, but to randomly sample nodes and run Monte Carlo simulations in opposite direction to search the nodes which can influence the sampled nodes. This motivates many studies to further improve the sampling technology [27]- [30] and memory consumption [31], [32].…”

Importance Sample-Based Approximation Algorithm for Cost-Aware Targeted Viral Marketing

“…IVM includes two components: generating IBS to estimate the benefit function and new strategy to find candidate solution and checks its approximation guarantee condition by developing two lower and upper bound functions. iterations (line [4][5][6][7][8][9][10][11][12][13][14]. In each iterator t, the algorithm maintains a set R t consists N 1 · 2 t−1 and finds a candidate solution S t by using Improve Greedy Algorithm (IGA) for Budgeted Maximum Coverage (BMC) problem [6].…”

“…Our algorithm, namely Importance samplebased for Viral Marketing (IVM), contains two innovative techniques: 1) We note that importance samples (in the space of all benefit samples) can be used to estimate the benefit function. This leads to a general result of using importance sketches to estimate the influence spread function for IM [12]. 2) Base on that we design a new strategy to check approximation guarantee condition of candidate solutions.…”