%AGreenberg, Craig%AMacaluso, Sebastian%AMonath, Nicholas%ADubey, Avinava%AFlaherty, Patrick%AZaheer, Manzil%AAhmed, Amr%ACranmer, Kyle%AMcCallum, Andrew%Anull Ed.%D2021%I %K %MOSTI ID: 10290571 %PMedium: X %TExact and Approximate Hierarchical Clustering with A* %XHierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with 10^12 trees to 10^15 trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than 10^1000 trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering. Country unknown/Code not availableOSTI-MSA