Sound and Solution-Complete CCBS

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.