document: A multiple tree algorithm for the efficient association of asteroid observations In this paper we examine the problem of efficiently finding sets of observations that conform to a given underlying motion model . While this problem is often phrased as a tracking problem , where it is called track initiation , it is useful in a variety of tasks where we want to find correspondences or patterns in spatial-temporal data . Unfortunately , this problem often suffers from a combinatorial explosion in the number of potential sets that must be evaluated . We consider the problem with respect to large-scale asteroid observation data , where the goal is to find associations among the observations that correspond to the same underlying asteroid . In this domain , it is vital that we can efficiently extract the underlying associations . We introduce a new methodology for track initiation that exhaustively considers all possible linkages . We then introduce an exact tree-based algorithm for tractably finding all compatible sets of points . Further , we extend this approach to use multiple trees , exploiting structure from several time steps at once . We compare this approach to a standard sequential approach and show how the use of multiple trees can provide a significant benefit .
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