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Jump Point Search Pathfinding in 4-connected Grids

Johannes Baum

TL;DR

The paper addresses efficient pathfinding on 4-connected grids by adapting Jump Point Search to 4-directions as JPS4. It introduces a horizontal-first canonical ordering, neighbor pruning with natural vs forced neighbors, and obstacle-driven jump points to prune search while preserving optimality, with a formal optimality proof based on turning points. Empirical results show JPS4 achieves significant speedups over A* in cluttered environments, while A* remains faster on open maps; results vary with path length and obstacle density, highlighting practical trade-offs. The work contributes a theoretically grounded, practically relevant alternative to A* for grid-based pathfinding in video games and robotics, with avenues for bounded jumps and density-aware hybridization.

Abstract

This work introduces JPS4, a novel pathfinding algorithm for 4-connected grid maps. JPS4 builds upon the Jump Point Search (JPS8) algorithm, originally designed for 8-connected environments. To achieve efficient pathfinding on 4-connected grids, JPS4 employs a canonical ordering and a successor function that enable online graph pruning. This reduces the search space by minimizing unnecessary node expansions. The core concept of JPS4 as well as JPS8 lies in the utilization of jump points. Strategically placed at obstacle corners, jump points prevent the search from overlooking crucial sections of the state space. They essentially reinitialize the canonical ordering, allowing exploration beyond obstacles. This mechanism ensures JPS4 finds optimal paths even in complex environments. The paper further explores the optimality of JPS4 and compares its performance against the established A* algorithm on various grid maps. Benchmarking results demonstrate that JPS4 significantly outperforms A* in scenarios with high obstacle density. However, A* remains more efficient on open maps. Overall, JPS4 presents itself as a promising alternative to A* for pathfinding on 4-connected grids, particularly applicable in video game development.

Jump Point Search Pathfinding in 4-connected Grids

TL;DR

The paper addresses efficient pathfinding on 4-connected grids by adapting Jump Point Search to 4-directions as JPS4. It introduces a horizontal-first canonical ordering, neighbor pruning with natural vs forced neighbors, and obstacle-driven jump points to prune search while preserving optimality, with a formal optimality proof based on turning points. Empirical results show JPS4 achieves significant speedups over A* in cluttered environments, while A* remains faster on open maps; results vary with path length and obstacle density, highlighting practical trade-offs. The work contributes a theoretically grounded, practically relevant alternative to A* for grid-based pathfinding in video games and robotics, with avenues for bounded jumps and density-aware hybridization.

Abstract

This work introduces JPS4, a novel pathfinding algorithm for 4-connected grid maps. JPS4 builds upon the Jump Point Search (JPS8) algorithm, originally designed for 8-connected environments. To achieve efficient pathfinding on 4-connected grids, JPS4 employs a canonical ordering and a successor function that enable online graph pruning. This reduces the search space by minimizing unnecessary node expansions. The core concept of JPS4 as well as JPS8 lies in the utilization of jump points. Strategically placed at obstacle corners, jump points prevent the search from overlooking crucial sections of the state space. They essentially reinitialize the canonical ordering, allowing exploration beyond obstacles. This mechanism ensures JPS4 finds optimal paths even in complex environments. The paper further explores the optimality of JPS4 and compares its performance against the established A* algorithm on various grid maps. Benchmarking results demonstrate that JPS4 significantly outperforms A* in scenarios with high obstacle density. However, A* remains more efficient on open maps. Overall, JPS4 presents itself as a promising alternative to A* for pathfinding on 4-connected grids, particularly applicable in video game development.
Paper Structure (11 sections, 2 theorems, 4 figures, 6 algorithms)

This paper contains 11 sections, 2 theorems, 4 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Notation and Terminology
  4. Algorithm
  5. Canonical Ordering
  6. Neighbor Pruning Rules
  7. Jump Points
  8. Optimality
  9. Benchmarks
  10. Results
  11. Conclusion and Future Work

Key Result

Lemma 4.1

Each turning point along an optimal horizontal-first path $\pi'$ is also a jump point.

Figures (4)

  • Figure 1: Elimination of symmetric paths in obstacle-free maps via canonical ordering.
  • Figure 2: Natural and forced neighbors for vertical movements (black square: obstacle, p: parent node, x: current node, nn: natural neighbor, fn?: potentially forced neighbor, fn: forced neighbor)
  • Figure 3: Jump points are introduced to make positions reachable that have become unreachable in our canonical ordering due to obstacles. Obstacles are marked as black squares, while jump points are represented through gray squares.
  • Figure 4: Average speedup of JPS4 compared to A* grouped by path length.

Theorems & Definitions (9)

  • Definition 4.1: Natural Neighbors
  • Definition 4.2: Forced Neighbors
  • Definition 4.3: Jump Point
  • Definition 4.4: Turning Point
  • Definition 4.5: Horizontal-First Path
  • Lemma 4.1
  • proof
  • Theorem 4.2
  • proof