Theoretical Results Regarding High Level Architecture Data Distribution Management Abstract: The High Level Architecture (HLA) is an architecture for constructing distributed simulations. The Data Distribution Management (DDM) services of HLA reduce the amount of data delivered to an HLA federate by allowing communications connections to be based on federates' expressions of data production and requirements. HLA Run-Time Infrastructure determines the data connections in a federation based on those expressions (called "matching") and configures the network infrastructure to deliver data along those connections (called "connecting"). The definition of HLA in general, and DDM in particular, has changed from the previous DoD 1.3 version to the new IEEE 1516 version of the HLA specifications. Three theorems regarding HLA DDM are proven. Theorem 1: A lower bound for any algorithm performing HLA DDM matching is in ((n log n); this is proven by reduction from BINARY SEARCH. Theorem 2: The multicast grouping problem, which is often used for HLA DDM connecting, is NP-complete; this is proven by transformation from 3-PARTITION. Theorem 3: The new IEEE 1516 specification of HLA DDM is at least as powerful, in terms of representable configurations, as the old DoD 1.3 specification of HLA DDM; this is proven by exhibiting an equivalence-preserving transformation from DDM 1.3 configurations to DDM 1516 configurations. Biography: Mikel D. Petty is Chief Scientist of the Virginia Modeling, Analysis and Simulation Center of Old Dominion University. He worked previously at the University of Central Florida's Institute for Simulation and Training. He has been performing and leading modeling and simulation research since 1990. He received a Ph.D. from the University of Central Florida (UCF) in 1997, an M.S. from UCF in 1988, and a B.S. from the California State University Sacramento in 1980, all in Computer Science. His research interests are in distributed simulation interoperability, computer generated forces, multi-resolution simulation, and applications of computational geometry to simulation. During 10 years in the research field he has published 80 research papers in those areas and has been awarded over 35 research contracts.