Cognition · Software component
Geometric Distance Heuristic
Software componentCognitionCognition & Memoryarc:GeometricDistanceHeuristic
A heuristic estimator that computes closed-form geometric distance (Manhattan, Euclidean or Chebyshev) from a state's coordinates to the goal's, assuming obstacle-free movement.
Responsibility. Computes an optimistic closed-form distance-to-goal estimate in constant time.
Also known as: Manhattan distance heuristic, Euclidean distance heuristic, Chebyshev distance heuristic
Variant of Heuristic Estimator abstract
When to choose. Choose when state coordinates are available and per-node evaluation must be near-free; the sweet spot for grid and road pathfinding.
Relationships
alternative to variability
Design guidance
- SHOULD match the distance metric to the permitted movement model (Manhattan for 4-directional grids, Chebyshev for 8-directional, Euclidean for free or diagonal movement).
Quantitative guidance
As stated by the sources; verify before use.
- Manhattan distance computed in 0.3 microseconds; 380 expansions cost 114 microseconds, <1% of search time (Ch5.6).
- Manhattan typically underestimates true cost by 15-30% (Ch5.6).
Classification
- Patterns
- Manhattan distance (4-directional movement)Euclidean distance (any-direction/diagonal movement)Chebyshev distance (8-directional movement)
- Quality attributes
- Performance efficiency (ISO/IEC 25010)Maintainability (ISO/IEC 25010)
Sources
- Ch5.6: T. Nguyen, "A* Search and Replaning," in Mastering Agentic AI Systems: Guide for the NVIDIA NCP-AAI Exam, 1st ed. 2026, ch. 5.6. ISBN: 9798244538229.