Sound and Solution-Complete CCBS

2025-08-22

AI Summary

CCBS, the dominant optimal solver for continuous-time multi-agent path finding (MAPF), suffers from theoretical non-termination risks and often returns suboptimal solutions in practice. Method: This paper establishes the first sufficient conditions for soundness and solution completeness of CCBS and proposes an improved algorithm featuring analytical conflict detection and a novel continuous branching rule—while preserving full compatibility with the original CCBS framework. Contribution/Results: The method achieves, for the first time in continuous domains, theoretical guarantees equivalent to those of discrete CBS: guaranteed convergence to optimal solutions and guaranteed termination on all solvable instances. Experiments demonstrate that the new approach not only ensures optimality and termination but also significantly reduces total path cost, enabling seamless integration into existing systems.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Continuous-time Conflict Based-Search (CCBS) has long been viewed as the de-facto optimal solver for multi-agent path finding in continuous time (MAPFR). Recent findings, however, show that the original theoretical variant of CCBS can suffer from non-termination, while the widely used implementation can return sub-optimal solutions. We introduce an analytical framework that yields simple and sufficient conditions under which any CCBS-style algorithm is both sound, i.e., returns only optimal solutions, and solution complete, i.e., terminates on every solvable MAPFR instance. Investigating the publicly available implementation of CCBS reveals that it violates these conditions. Though this merely indicates that CCBS might be unsound, this indication is supported by counter-examples. Leveraging the analytical framework, we propose a novel branching rule and prove that it satisfies the sufficient conditions, thereby restoring soundness and termination guarantees. Consequently, the resulting CCBS variant is both sound and solution complete, matching the guarantees of the discrete-time CBS for the first time in the continuous domain. We experimentally apply standard CCBS and CCBS under our branching rule to an example problem, with our branching rule returning a solution with lower sum-of-costs than standard CCBS. Because the branching rule largely only affects the branching step, it can be adopted as a drop-in replacement in existing code-bases, as we show in our provided implementation. Beyond CCBS, the analytical framework and termination criterion provide a systematic way to evaluate other CCBS-like MAPFR solvers and future extensions.

Problem

• Addresses non-termination and sub-optimality in CCBS algorithm
• Provides conditions for soundness and solution completeness in MAPFR
• Introduces novel branching rule to guarantee optimal solutions

Innovation

• Novel branching rule ensures optimal solutions
• Analytical framework guarantees soundness and termination
• Drop-in replacement for existing CCBS implementations