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What kind of heuristics are useful in a tree decomposition of a graph to find the k shortest paths from a given source to a vertex?

Moreover, the local shortest paths at each node in a tree are precomputed. Here, the graph is undirected and weighted. I'm interested in finding only simple paths, i.e., no nodes are repeated in a path.

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    $\begingroup$ Is your question what heuristics are there to find a tree decomposition, or what heuristics are there to find the shortest paths given that you have a tree decomposition? $\endgroup$ – Luke Mathieson Jan 8 '13 at 0:54
  • $\begingroup$ yah. i suppose to know about heuristics to find the shortest paths given i have a tree decomposition. $\endgroup$ – NRK Jan 8 '13 at 16:09

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