The asynchronous committee meeting problem
The committee meeting problem consists in finding the earliest meeting time acceptable to every member of a committee. We consider an asynchronous version of the problem that does not presuppose the existence of a global clock, where meeting times are maximal antichains in a poset of ‘local times’, and propose an efficient algorithm to solve it. A generalization, the private meeting problem, where the earliest time for a meeting without some committee members is sought, turns out to be NP-complete. However, it can be solved in polynomial time if the poset is N-free, that is, representing a precedence of the arcs (and not the nodes) of an acyclic directed graph. This special case is relevant, because it allows to improve the key algorithm of the model checking technique developed in  for Petri nets.
Key wordsCommittee meeting problem maximal antichains N-free posets Petri net unfolding
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