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- W1986349862 abstract "Given a digraph G=(V, E) and a cost function C:E→R, which does not imply negative cost cycles, let us denote by G(δ) the graph obtained from G by adding to the cost of each edge the positive constant δ; then we want to compute the cost of the least cost path from a given origin r to each node v in the graph G(δ) for different choices of δ⩾0, without having to run a least cost path algorithm everytime with a new cost function. Through a preprocessing of the given digraph based on the Bellmann–Ford algorithm, we will be able to obtain in time O(λ(|E|+|V|) the necessary information to generate a structure that will allow us to answer each query in time O(log λ), where λ is defined to be the length of the longest least cost path in the digraph. In particular, we will see that the only possible candidates to become least cost paths in a graph G(δ) are the least cost paths of bounded length in the original graph G; further, we will show that finding which of these candidates will become least cost path in a G(δ) and for which δ is equivalent to finding the lower envelope of at most λ lines, which, in turn, can be reduced to the lower convex hull problem for a set of ordered points." @default.
- W1986349862 created "2016-06-24" @default.
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- W1986349862 date "1991-09-01" @default.
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- W1986349862 title "A special case of the dynamization problem for least cost paths" @default.
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- W1986349862 doi "https://doi.org/10.1016/0020-0190(91)90002-y" @default.
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