# Towards Optimal Strategy for Adaptive Probing in Incomplete Networks

## TL;DR

This paper studies an adaptive network probing problem where an agent aims to maximize explored nodes with limited probes, establishing theoretical hardness and proposing learning-based strategies that outperform heuristics.

## Contribution

It introduces a novel formulation of the adaptive probing problem, proves its strong inapproximability, and develops learning frameworks that effectively learn strategies for different networks.

## Key findings

- Proves no finite approximation ratio algorithm exists unless P=NP.
- Designs learning frameworks that outperform existing heuristics.
- Demonstrates the effectiveness of learned strategies through extensive experiments.

## Abstract

We investigate a graph probing problem in which an agent has only an incomplete view $G' \subsetneq G$ of the network and wishes to explore the network with least effort. In each step, the agent selects a node $u$ in $G'$ to probe. After probing $u$, the agent gains the information about $u$ and its neighbors. All the neighbors of $u$ become \emph{observed} and are \emph{probable} in the subsequent steps (if they have not been probed). What is the best probing strategy to maximize the number of nodes explored in $k$ probes? This problem serves as a fundamental component for other decision-making problems in incomplete networks such as information harvesting in social networks, network crawling, network security, and viral marketing with incomplete information. While there are a few methods proposed for the problem, none can perform consistently well across different network types. In this paper, we establish a strong (in)approximability for the problem, proving that no algorithm can guarantees finite approximation ratio unless P=NP. On the bright side, we design learning frameworks to capture the best probing strategies for individual network. Our extensive experiments suggest that our framework can learn efficient probing strategies that \emph{consistently} outperform previous heuristics and metric-based approaches.