Exact Computation of Influence Spread by Binary Decision Diagrams

TL;DR

This paper introduces the first exact algorithm for influence spread calculation in social networks under the independent cascade model, using binary decision diagrams to enable precise computation where previous methods relied on approximations.

Contribution

The paper presents a novel algorithm that constructs BDDs for exact influence spread computation, improving accuracy and enabling new related influence analysis tasks.

Findings

Successfully computed influence spread on real-world networks with hundreds of edges

Demonstrated the algorithm's efficiency over naive methods

Compared exact results with Monte-Carlo approximations to evaluate accuracy

Abstract

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.