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On the Completeness of Conflict-Based Search: Temporally-Relative Duplicate Pruning

Thayne T Walker, Nathan R Sturtevant

TL;DR

This work addresses the long-standing incompleteness of Conflict-Based Search (CBS) in unsolvable MAPF instances by introducing Temporally-Relative Duplicate Pruning (TRDP). TRDP detects temporally-relative duplicates to prune multi-agent loops, rendering CBS complete for classic MAPF and MAPFQ, with applicability extended to MAPFR. Theoretical results show TRDP preserves optimality and ensures finite search space, while a bypass mechanism mitigates branch explosion in dense settings. Empirically, TRDP incurs minimal overhead in typical cases and can significantly prune search in agent-dense scenarios, offering a practical route to native completeness without parallel complete solvers. Overall, TRDP provides a simple, robust enhancement to CBS that guarantees termination and maintains performance in common MAPF domains, with promising implications for more complex continuous-time formulations.

Abstract

Conflict-Based Search (CBS) algorithm for the multi-agent pathfinding (MAPF) problem is that it is incomplete for problems which have no solution; if no mitigating procedure is run in parallel, CBS will run forever when given an unsolvable problem instance. In this work, we introduce Temporally-Relative Duplicate Pruning (TRDP), a technique for duplicate detection and removal in both classic and continuous-time MAPF domains. TRDP is a simple procedure which closes the long-standing theoretic loophole of incompleteness for CBS by detecting and avoiding the expansion of duplicate states. TRDP is shown both theoretically and empirically to ensure termination without a significant impact on runtime in the majority of problem instances. In certain cases, TRDP is shown to increase performance significantly

On the Completeness of Conflict-Based Search: Temporally-Relative Duplicate Pruning

TL;DR

This work addresses the long-standing incompleteness of Conflict-Based Search (CBS) in unsolvable MAPF instances by introducing Temporally-Relative Duplicate Pruning (TRDP). TRDP detects temporally-relative duplicates to prune multi-agent loops, rendering CBS complete for classic MAPF and MAPFQ, with applicability extended to MAPFR. Theoretical results show TRDP preserves optimality and ensures finite search space, while a bypass mechanism mitigates branch explosion in dense settings. Empirically, TRDP incurs minimal overhead in typical cases and can significantly prune search in agent-dense scenarios, offering a practical route to native completeness without parallel complete solvers. Overall, TRDP provides a simple, robust enhancement to CBS that guarantees termination and maintains performance in common MAPF domains, with promising implications for more complex continuous-time formulations.

Abstract

Conflict-Based Search (CBS) algorithm for the multi-agent pathfinding (MAPF) problem is that it is incomplete for problems which have no solution; if no mitigating procedure is run in parallel, CBS will run forever when given an unsolvable problem instance. In this work, we introduce Temporally-Relative Duplicate Pruning (TRDP), a technique for duplicate detection and removal in both classic and continuous-time MAPF domains. TRDP is a simple procedure which closes the long-standing theoretic loophole of incompleteness for CBS by detecting and avoiding the expansion of duplicate states. TRDP is shown both theoretically and empirically to ensure termination without a significant impact on runtime in the majority of problem instances. In certain cases, TRDP is shown to increase performance significantly
Paper Structure (12 sections, 6 theorems, 3 equations, 4 figures, 3 tables, 3 algorithms)

This paper contains 12 sections, 6 theorems, 3 equations, 4 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Definition
  3. Background and Motivation
  4. Completeness of CBS
  5. Mechanics of Duplicate Detection
  6. Duplicate Pruning in CBS
  7. CBS
  8. CBS+TRDP
  9. Theoretical Analysis
  10. Bypassing TRD Splits
  11. Empirical Results
  12. Conclusion

Key Result

Lemma 3

An optimal path cannot contain a loop.

Figures (4)

  • Figure 1: An unsolvable MAPF instance where the agents must swap places.
  • Figure 2: A MAPF instance that becomes unsolvable in MAPFR with larger agents.
  • Figure 3: (a) An unsolvable MAPF instance and (b) a partial CBS high-level search tree with TRDP.
  • Figure 4: (a) A solvable MAPFR instance and (b) a partial CBS high-level search tree with TRDP.

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Lemma 3
  • proof
  • Corollary 4
  • Lemma 5
  • proof
  • Lemma 6
  • proof
  • Theorem 7
  • ...and 3 more