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Suppose we are given a graph with distances for each of the edges and merit for each of the nodes. What are the best (approximation) algorithms for computing the the most meritorious simple path with a cap on the maximum distance allowed?

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    $\begingroup$ Related: cstheory.stackexchange.com/q/25922/2150 $\endgroup$ – Marcus Ritt Dec 26 '14 at 8:45
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    $\begingroup$ Orienteering refers to the problem where one wants a walk with a given budget instead of a simple path - a node is allowed to be visited more than once but the merit/profit is only counted once. If distances satisfy triangle inequality then asking for a simple path is equivalent to asking for a walk. However, if you insist on a simple path then what you are looking for is closely related to the longest path problem. For longest paths check Gabow's paper and pointers: epubs.siam.org/doi/abs/10.1137/… $\endgroup$ – Chandra Chekuri Dec 27 '14 at 4:26

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