# Efficient Approximation Algorithms for Adaptive Seed Minimization

## TL;DR

This paper introduces ASTI, an efficient adaptive seed minimization algorithm that selects seed nodes in multiple batches to influence a target number of users in social networks, with proven approximation guarantees.

## Contribution

The paper presents the first adaptive seed minimization algorithm with provable approximation guarantees and practical efficiency, outperforming existing non-adaptive methods.

## Key findings

- ASTI achieves near-optimal influence with fewer seed nodes.
- ASTI runs in expected polynomial time, scalable to large networks.
- Experimental results show ASTI outperforms competing algorithms in effectiveness and efficiency.

## Abstract

As a dual problem of influence maximization, the seed minimization problem asks for the minimum number of seed nodes to influence a required number $\eta$ of users in a given social network $G$. Existing algorithms for seed minimization mostly consider the non-adaptive setting, where all seed nodes are selected in one batch without observing how they may influence other users. In this paper, we study seed minimization in the adaptive setting, where the seed nodes are selected in several batches, such that the choice of a batch may exploit information about the actual influence of the previous batches. We propose a novel algorithm, ASTI, which addresses the adaptive seed minimization problem in $O\Big(\frac{\eta \cdot (m+n)}{\varepsilon^2}\ln n \Big)$ expected time and offers an approximation guarantee of $\frac{(\ln \eta+1)^2}{(1 - (1-1/b)^b) (1-1/e)(1-\varepsilon)}$ in expectation, where $\eta$ is the targeted number of influenced nodes, $b$ is size of each seed node batch, and $\varepsilon \in (0, 1)$ is a user-specified parameter. To the best of our knowledge, ASTI is the first algorithm that provides such an approximation guarantee without incurring prohibitive computation overhead. With extensive experiments on a variety of datasets, we demonstrate the effectiveness and efficiency of ASTI over competing methods.