LLM-Aided A* Search in Non-Geometric Network Graphs

2026-06-22

AI Summary

This work addresses the inefficiency of traditional heuristic search in graphs where edge weights represent non-geometric metrics such as latency or cost, due to the absence of effective heuristics. It proposes the first integration of large language models (LLMs) into non-geometric graph path planning by coupling them with the A* algorithm. The approach leverages graph structural features and landmark-based distances—inspired by the ALT heuristic—as input to the LLM to generate intermediate waypoints that guide the search direction. Notably, this method restores the LLM’s awareness of target distance without requiring complex prompt engineering. Experimental results across diverse graph topologies with up to 2,000 nodes demonstrate that the proposed technique reduces the number of expanded nodes by approximately 50% while incurring only a marginal increase in path cost, thereby significantly enhancing search efficiency and validating its practicality and effectiveness.

Abstract

Finding the shortest path in non-geometric network graphs, where edge weights encode arbitrary metrics such as latency or monetary cost rather than spatial distance, poses a challenge for informed search algorithms. Their efficiency depends on an informative heuristic, typically supplied in spatial domains by geometric distances that have no counterpart on non-geometric graphs. We propose a large language model (LLM)-aided A* algorithm in which an LLM generates intermediate waypoints that guide the A* expansion toward promising graph regions. At the core of the approach are landmark distances, which serve both as an admissible landmark-based (ALT) heuristic for the search and as a compact structural feature that, supplied to the LLM, restores the distance-to-destination signal it would otherwise lack on non-geometric graphs. Our comprehensive experiments on multiple graph topologies with up to 2,000 nodes demonstrate that LLM-generated waypoints reduce the number of expanded nodes by around 50% while incurring only a marginal path cost increase compared to the optimal solution. We further analyze the impact of prompt engineering and show that incorporating compact structural features, namely heuristic estimates, is more effective than advanced prompting techniques. These findings demonstrate the potential of combining LLM- based guidance with classical search algorithms for efficient network optimization.

Problem

• non-geometric graphs
• shortest path
• informed search
• heuristic
• network optimization

Innovation

• LLM-aided search
• non-geometric graphs
• A* algorithm
• landmark-based heuristic
• waypoint guidance