Coordinating time-constrained multi-agent resource sharing with fault detection

Sharing common resources in a distributed multi-agent environment requires coordination to avoid faulty system states. The statuses of resources such as personnel, equipments, and environmental factors at a point in time determine the system state at that time. When an agent takes an action at any time point within a scheduled time interval, it becomes a state-transition event occurring at that time. For each event, the underlying state transition relation can be compactly encoded as causal rules, which describe how statuses of resources and environmental factors may change in different ways based on preconditions before the event occurs. The central coordinator needs to check in advance whether any of the possible event sequences consistent with a proposed schedule may end in faulty system states. This fault detection task is NP-complete even for a polynomial-size state space in general. In this paper, we investigate the computational complexity of the fault detection task when agents fairly constrain the maximal length of time intervals. We develop a decomposition algorithm to divide the fault detection task over all events into subtasks involving subsets of the events with overlapping time intervals. For each subtask, only a subspace with reduced dimensionality is involved instead of the whole original state space. When the maximal length of time intervals is constrained below a fair threshold, we prove that with probability approaching one as the size of the problem instance grows the algorithm can accomplish the fault detection task in polynomial time even if the original underlying state space is exponential in size.