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Conflict-Based Search

Conflict-Based Search addresses multi-agent pathfinding by splitting conflicts into constraints and solving constrained paths for each agent.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Pathfinding
Difficulty: Advanced
Family: Multi-Agent Pathfinding
Tier: Specialized
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 0
Relationships: 2
Code example: Not ready
Visualization: Ready

Overview

Conflict-Based Search is a multi-agent pathfinding method for multi-agent pathfinding. It works by splitting conflicts into constraints and solving constrained paths for each agent.

Core Concepts

multi-agent pathfindingclause learningpathfinding

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(1)

Average

O(n)

Worst

O(n)

Space

O(1)

When to Use

Use Conflict-Based Search when solving multi-agent pathfinding and you want to benefit from splitting conflicts into constraints and solving constrained paths for each agent.
Choose it when O(n) average/worst-case time and O(1) memory match your workload profile.
Prefer it over Visibility Graph Roadmap or 0-1 BFS when the problem structure favors multi-agent pathfinding.

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 multi-agent pathfinding within Multi-Agent Pathfinding workloads (O(n) time, O(1) space).
Works by splitting conflicts into constraints and solving constrained paths for each agent.
Maintains key invariants across multi-agent pathfinding, clause learning, pathfinding.

Use Cases

Production and research workloads requiring multi-agent pathfinding via splitting conflicts into constraints and solving constrained paths for each agent.
Multi-Agent Pathfinding pipelines where O(n) time and O(1) space fit system constraints.
Engineering comparisons against Visibility Graph Roadmap and 0-1 BFS when tuning multi-agent pathfinding.

Inputs

Grid/graph G = (V, E) and k agents with individual (start_i, goal_i) pairs

Outputs

Collision-free time-indexed paths π_1..π_k minimizing total arrival cost

Pseudocode

1.Initialize the search space, start/goal states, and cost/priority tables for Conflict-Based Search.
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 splitting conflicts into constraints and solving constrained paths for each agent.
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: Grid/graph G = (V, E) and k agents with individual (start_i, goal_i) pairs configured for a representative multi-agent pathfinding test case
Output: Collision-free time-indexed paths π_1..π_k minimizing total arrival cost satisfying Conflict-Based Search invariants
Explanation: Conflict-Based Search processes the input by splitting conflicts into constraints and solving constrained paths for each agent, tracking multi-agent pathfinding and clause learning to produce the verified multi-agent 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 & Trajectory

Show splitting conflicts into constraints and solving constrained paths for each agent on a small multi-agent pathfinding example.

Step 1 of 5: Initialize the search space, start/goal states, and cost/priority tables for Conflict-Based Search.

pathfinding-mechanism

Notes

Conflict-Based Search operates in O(n) time and O(1) space within the Multi-Agent Pathfinding family. Often compared with Visibility Graph Roadmap and 0-1 BFS.