Overview
Visibility Graph Roadmap handles shortest path among obstacles by connecting mutually visible obstacle vertices and searching the resulting graph.
CoreSource checked
Visibility Graph Roadmap
Visibility Graph Roadmap handles shortest path among obstacles by connecting mutually visible obstacle vertices and searching the resulting graph.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Pathfinding
- Difficulty
- Intermediate
- Family
- Geometric Pathfinding
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 5
- Code example
- Ready
- Visualization
- Ready
Core Concepts
shortest path among obstaclesgeometric pathfindingpathfinding
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(V + E)
Average
O((V + E) log V)
Worst
O(V^2 + E)
Space
O(V + E)
When to Use
- Use Visibility Graph Roadmap when solving geometric pathfinding and you want to benefit from connecting mutually visible obstacle vertices and searching the resulting graph.
- Choose it when O((V + E) log V) average/worst-case time and O(V + E) memory match your workload profile.
- Prefer it over 0-1 BFS or Dial's Algorithm when the problem structure favors shortest path among obstacles.
When Not to Use
- Avoid when path costs or obstacles change in ways the method cannot update efficiently.
- Avoid when approximate paths are unacceptable and the method does not guarantee optimality.
What It Does
- Computes geometric pathfinding within Geometric Pathfinding workloads (O((V + E) log V) time, O(V + E) space).
- Works by connecting mutually visible obstacle vertices and searching the resulting graph.
- Maintains key invariants across shortest path among obstacles, geometric pathfinding, pathfinding.
Use Cases
- Production and research workloads requiring geometric pathfinding via connecting mutually visible obstacle vertices and searching the resulting graph.
- Geometric Pathfinding pipelines where O((V + E) log V) time and O(V + E) space fit system constraints.
- Engineering comparisons against 0-1 BFS and Dial's Algorithm when tuning geometric pathfinding.
Inputs
- Start point, goal point, and polygonal obstacle vertices in 2D plane
Outputs
- Euclidean shortest piecewise-linear path around obstacle corners
Pseudocode
- 1.Initialize the search space, start/goal states, and cost/priority tables for Visibility Graph Roadmap.
- 2.Insert the initial state into the open frontier or roadmap with its baseline cost and heuristic estimate.
- 3.Expand or sample candidate transitions by connecting mutually visible obstacle vertices and searching the resulting graph.
- 4.Update path costs, parent pointers, or conflict constraints whenever an improved trajectory is found.
- 5.Reconstruct and return the collision-free path from start to goal once the termination criterion holds.
Canonical Example
- Input
- Start point, goal point, and polygonal obstacle vertices in 2D plane configured for a representative geometric pathfinding test case
- Output
- Euclidean shortest piecewise-linear path around obstacle corners satisfying Visibility Graph Roadmap invariants
- Explanation
- Visibility Graph Roadmap processes the input by connecting mutually visible obstacle vertices and searching the resulting graph, tracking shortest path among obstacles and geometric pathfinding to produce the verified geometric pathfinding result.
Implementation Notes
- Separate search state from world state so changes can be tested.
- Use small maps with known optimal answers before large scenarios.
- Track whether returned paths are optimal, bounded, or heuristic.
Common Pitfalls
- Using an inadmissible heuristic where optimality is expected.
- Ignoring dynamic obstacles, time-dependent costs, or changing edge weights.
- Testing only open grids and missing narrow-passage cases.
Interactive Mechanism Walkthrough
2D Grid Wavefront & TrajectoryShow connecting mutually visible obstacle vertices and searching the resulting graph on a small shortest path among obstacles example.
S
#
#
#
#
#
#
#
G
Step 1 of 5: Initialize the search space, start/goal states, and cost/priority tables for Visibility Graph Roadmap.
pathfinding-mechanismNotes
Visibility Graph Roadmap operates in O((V + E) log V) time and O(V + E) space within the Geometric Pathfinding family. Often compared with 0-1 BFS and Dial's Algorithm.
Sources (1)
What each reference supports for this entry.
Planning Algorithms
BookMotion-planning reference covering Visibility Graph Roadmap roadmap, visibility, or sampling-based search construction.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Conceptual neighbor0-1 BFS
Pathfinding · Core
Visibility Graph Roadmap and 0-1 BFS both relate to shortest path among obstacles, but use different structures or assumptions.
Compare with thisRelationships
View full relationship pageConceptual neighbor0-1 BFS
Visibility Graph Roadmap and 0-1 BFS both relate to shortest path among obstacles, but use different structures or assumptions.
Conceptual neighborDial's Algorithm
Visibility Graph Roadmap and Dial's Algorithm both relate to shortest path among obstacles, but use different structures or assumptions.
Conceptual neighborEppstein K Shortest Paths
Visibility Graph Roadmap and Eppstein K Shortest Paths both relate to shortest path among obstacles, but use different structures or assumptions.
Tags
PathfindingGraph