Approximation Analysis of Influence Spread in Social Networks

TL;DR

This paper explores approximation algorithms for influence spread problems in social networks, focusing on minimizing seed sets for target coverage and minimizing propagation time under resource constraints.

Contribution

It introduces new approximation algorithms for MINTSS and MINTIME, addressing their NP-hardness and providing bicriteria solutions with theoretical bounds.

Findings

Greedy algorithm for MINTSS achieves bicriteria approximation.

Exact polynomial-time solution for MINTIME with logarithmic budget boost.

Heuristic comparisons demonstrate the effectiveness of proposed algorithms.

Abstract

In the context of influence propagation in a social graph, we can identify three orthogonal dimensions - the number of seed nodes activated at the beginning (known as budget), the expected number of activated nodes at the end of the propagation (known as expected spread or coverage), and the time taken for the propagation. We can constrain one or two of these and try to optimize the third. In their seminal paper, Kempe et al. constrained the budget, left time unconstrained, and maximized the coverage: this problem is known as Influence Maximization. In this paper, we study alternative optimization problems which are naturally motivated by resource and time constraints on viral marketing campaigns. In the first problem, termed Minimum Target Set Selection (or MINTSS for short), a coverage threshold n is given and the task is to find the minimum size seed set such that by activating it, at least n nodes are eventually activated in the expected sense. In the second problem, termed MINTIME, a coverage threshold n and a budget threshold k are given, and the task is to find a seed set of size at most k such that by activating it, at least n nodes are activated, in the minimum possible time. Both these problems are NP-hard, which motivates our interest in their approximation. For MINTSS, we develop a simple greedy algorithm and show that it provides a bicriteria approximation. We also establish a generic hardness result suggesting that improving it is likely to be hard. For MINTIME, we show that even bicriteria and tricriteria approximations are hard under several conditions. However, if we allow the budget to be boosted by a logarithmic factor and allow the coverage to fall short, then the problem can be solved exactly in PTIME. Finally, we show the value of the approximation algorithms, by comparing them against various heuristics.