This paper proposes two coordinates-based approaches for predicting Internet network distance in a peer-to-peer architecture: the triangulated heuristic and Global Network Positioning (GNP). The triangulated heuristic uses relative coordinates based on distances to base nodes, while GNP uses absolute coordinates derived from modeling the Internet as a geometric space. Both approaches allow end hosts to compute inter-host distances instantly upon discovering each other, making them scalable and efficient. Experiments using measured Internet distance data show that both approaches are more accurate than the existing state-of-the-art system IDMaps, with GNP achieving the highest accuracy and robustness. GNP is particularly effective in predicting short distances and is less affected by outliers. The paper also discusses the benefits of using peer-to-peer architectures over client-server solutions, including scalability and reduced communication overhead. It compares the performance of the three approaches in terms of measurement cost, communication cost, computation cost, and deployment. The results show that GNP outperforms the other two approaches in accuracy and robustness, especially in predicting short distances. The paper also explores the use of GNP in various applications, such as overlay routing and proxy location services, and discusses the impact of different error measurement functions and geometric space models on prediction accuracy.This paper proposes two coordinates-based approaches for predicting Internet network distance in a peer-to-peer architecture: the triangulated heuristic and Global Network Positioning (GNP). The triangulated heuristic uses relative coordinates based on distances to base nodes, while GNP uses absolute coordinates derived from modeling the Internet as a geometric space. Both approaches allow end hosts to compute inter-host distances instantly upon discovering each other, making them scalable and efficient. Experiments using measured Internet distance data show that both approaches are more accurate than the existing state-of-the-art system IDMaps, with GNP achieving the highest accuracy and robustness. GNP is particularly effective in predicting short distances and is less affected by outliers. The paper also discusses the benefits of using peer-to-peer architectures over client-server solutions, including scalability and reduced communication overhead. It compares the performance of the three approaches in terms of measurement cost, communication cost, computation cost, and deployment. The results show that GNP outperforms the other two approaches in accuracy and robustness, especially in predicting short distances. The paper also explores the use of GNP in various applications, such as overlay routing and proxy location services, and discusses the impact of different error measurement functions and geometric space models on prediction accuracy.