What question did this study set out to answer?

To establish the preprocessing requirements for distance oracles in n×n grid graphs under the Strong Exponential Time Hypothesis.

February 8, 2026Open Access

Conditional Lower Bounds for Grid Pathfinding Oracles

Key Points

To establish the preprocessing requirements for distance oracles in n×n grid graphs under the Strong Exponential Time Hypothesis.
Proved through reduction from the Orthogonal Vectors problem
Used explicit gadget construction to demonstrate the bounds
Any distance oracle requires Ω(n^(2-o(1))) preprocessing time
Achieving O(1) query time is expensive in terms of preprocessing
Provides justification for algorithms like Jump Point Search with O(n²) preprocessing and O(path length) query time

Abstract

This paper proves that, assuming the Strong Exponential Time Hypothesis (SETH), any distance oracle for n×n grid graphs with O (1) query time requires Ω (n^ (2-o (1) ) ) preprocessing time. The proof proceeds by reduction from the Orthogonal Vectors (OV) problem via an explicit gadget construction. The main result establishes a fundamental space-time tradeoff: achieving constant-time distance queries on grids is provably expensive in preprocessing. This provides theoretical justification for the design of practical pathfinding algorithms like Jump Point Search (JPS+), which achieve O (n²) preprocessing with O (path length) query time.

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Cite This Study

David R. Dudas (Thu,) studied this question.

synapsesocial.com/papers/698827c90fc35cd7a8846cd1 https://doi.org/https://doi.org/10.5281/zenodo.18498774

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