Multi-Agent Plan Recognition (MAPR) seeks to identify the dynamic team structures and team behaviors from the observations of the activity-sequences of a set of intelligent agents, based on a library of known team-activities (plan library). It has important applications in analyzing data from automated monitoring, surveillance, and intelligence analysis in general. In this paper, we formalize MAPR using a basic model that explicates the cost of abduction in single agent plan recognition by "flattening" or decompressing the (usually compact, hierarchical) plan library. We show that single-agent plan recognition with a decompressed library can be solved in time polynomial in the input size, while it is known that with a compressed (by partial ordering constraints) library it is NP-complete. This leads to an important insight: that although the compactness of the plan library plays an important role in the hardness of single-agent plan recognition (as recognized in the existing literature), that is not the case with multiple agents. We show, for the first time, that MAPR is NP-complete even when the (multi-agent) plan library is fully decompressed. As with previous solution approaches, we break the problem into two stages: hypothesis generation and hypothesis search. We show that Knuth's ``Algorithm X'' (with the efficient ``dancing links'' representation) is particularly suited for our model, and can be adapted to perform a branch and bound search for the second stage, in this model. We show empirically that this new approach leads to significant pruning of the hypothesis space in MAPR.