Sound and Solution-Complete CCBS

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.