The foregoing chapter introduced three local computation algorithms for the solution of single-query inference problems, among which the generalized collect algorithm was shown to be the most universal and efficient scheme. We therefore take this algorithm as the starting point for our study of the second class of local computation procedures that solve multi-query inference problems. Clearly, the most simple approach to compute multiple queries is to execute the collect algorithm repeatedly for each query. Since we already gave a general definition of a covering join tree that takes an arbitrary number of queries into account, it is not necessary to take a new join tree for the answering of a second query on the same knowledgebase. Instead, we redirect and renumber the join tree in such a way that its root node covers the current query and execute the collect algorithm. This procedure is repeated for each query. In Figure 3.15, arrows indicate the direction of the message-passing for a particular root node and therefore reflect the restrictions imposed on the node numbering. It is easy to see that changing the root node only affects the arrows between the old and the new root node. This is shown in Figure 4.1 where we also observe that a valid node numbering for the redirected join tree is obtained by inverting the numbering on the path between the old and the new root node. Hence, it is possible to solve a multi-query inference problem by ...

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