CBS with Continuous-Time Revisit

Abstract: Multi-Agent Path Finding in Continuous Time (\mapfr) extends the classical MAPF problem by allowing agents to operate in continuous time. Conflict-Based Search with Continuous Time (CCBS) is a foundational algorithm for solving \mapfr optimally. In this paper, we revisit the theoretical claims of CCBS and show the algorithm is incomplete, due to an uncountably infinite state space created by continuous wait durations. Through theoretical analysis and counter-examples, we examine the inherent challenges of extending existing MAPF solvers to address \mapfr while preserving optimality guarantees. By restricting waiting duration to fixed amounts, we identify a related sub-problem on graphs, \mapfrdt which we show is optimally solvable, including by CCBS. It remains an open question whether similar models exist for \mapfrct, a generalised version of \mapfrdt that allows arbitrary wait times, and \mapfrcs, which further allows arbitrary movements in continuous space.