A Structural Complexity Heuristic for Admissible Shortest Path Optimization HFP-A*

Optimizing Dijkstra: A Parallel Hybrid Model Using a Prime Factor Heuristic (HFP) for Admissible Acceleration

Dijkstra's algorithm provides an optimal solution to the Shortest Path Problem (SPP) but relies on a "blind" search strategy. We introduce a new, non-geometric heuristic class, the HFP (Heuristic of Prime Factors), which guides an A* search based on the structural complexity of nodes, defined by the number of their distinct prime factors ω(n)≠2

We demonstrate that this heuristic's correlation with the optimal path is an emergent property that appears only in graphs of sufficient complexity. However, our key finding is that the HFP heuristic is not infallible. Our batch tests revealed "landmine" scenarios (approx. 10-20% of cases) where the heuristic is catastrophically misleading, causing the A* search to explore more steps than a blind Dijkstra (e.g., 6,425 steps vs. 1,533).

Therefore, a "naive" HFP-A* implementation is unreliable. We propose a Parallel Hybrid Algorithm as the only robust and admissible solution. This algorithm runs a "blind" Dijkstra on one thread and our "guided" HFP-A* on another. The first thread to find the solution "wins" (terminates the other).

This hybrid model is 100% precise (it is mathematically impossible for it to be slower than standard Dijkstra) and wins the race 70-80% of the time, leveraging the HFP heuristic's 21.54% average step reduction in its winning cases. This method provides a reliable framework for achieving significant, real-world computational savings.

Andrés Sebastián Pirolo 2025

feedback: apirolo@abc.gob.ar

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Contact: apirolo@abc.gob.ar