# Scalable Bicriteria Algorithms for the Threshold Activation Problem in Online Social Networks

## TL;DR

This paper presents a scalable, parallelizable bicriteria algorithm for the Threshold Activation Problem in large social networks, balancing solution size and accuracy with provable guarantees.

## Contribution

Introduces the first scalable, parallel algorithm with performance guarantees for TAP that handles large datasets and incorporates external influence under certain conditions.

## Key findings

- Algorithm runs in near-linear time with respect to network size.
- Provides probabilistic guarantees on activation and seed set size.
- Applicable to general influence models including external influence.

## Abstract

We consider the Threshold Activation Problem (TAP): given social network $G$ and positive threshold $T$, find a minimum-size seed set $A$ that can trigger expected activation of at least $T$. We introduce the first scalable, parallelizable algorithm with performance guarantee for TAP suitable for datasets with millions of nodes and edges; we exploit the bicriteria nature of solutions to TAP to allow the user to control the running time versus accuracy of our algorithm through a parameter $\alpha \in (0,1)$: given $\eta > 0$, with probability $1 - \eta$ our algorithm returns a solution $A$ with expected activation greater than $T - 2 \alpha T$, and the size of the solution $A$ is within factor $1 + 4 \alpha T + \log ( T )$ of the optimal size. The algorithm runs in time $O \left( \alpha^{-2}\log \left( n / \eta \right) (n + m) |A| \right)$, where $n$, $m$, refer to the number of nodes, edges in the network. The performance guarantee holds for the general triggering model of internal influence and also incorporates external influence, provided a certain condition is met on the cost-effectivity of seed selection.