  This paper studies the interaction between knowledge, time and coordination
in systems in which timing information is available. Necessary conditions are
given for the causal structure in coordination problems consisting of
orchestrating a set of actions in a manner that satisfies a variety of temporal
ordering assumptions. Results are obtained in two main steps: A specification
of coordination is shown to require epistemic properties, and the causal
structure required to obtain these properties is characterised via "knowledge
gain" theorems. A new causal structure called a centibroom structure is
presented, generalising previous causal structures for this model. It is shown
to capture coordination tasks in which a sequence of clusters of events is
performed in linear order, while within each cluster all actions must take
place simultaneously. This form of coordination is shown to require the agents
to gain a nested common knowledge of particular facts, which in turn requires a
centibroom. Altogether, the results presented provide a broad view of the
causal shape underlying partially ordered coordinated actions. This, in turn,
provides insight into and can enable the design of efficient solutions to the
coordination tasks in question.
