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- W2150008165 abstract "Given a graph G=(V,E) and an integer D≥1, we consider the problem of augmenting G by the smallest number of new edges so that the diameter becomes at most D. It is known that no constant approximation algorithms to this problem with an arbitrary graph G can be obtained unless P=NP. For a forest G and an odd D≥3, it was open whether the problem is approximable within a constant factor. In this paper, we give the first constant factor approximation algorithm to the problem with a forest G and an odd D; our algorithm delivers an 8-approximate solution in O(|V|3) time. We also show that a 4-approximate solution to the problem with a forest G and an odd D can be obtained in linear time if the augmented graph is additionally required to be biconnected." @default.
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- W2150008165 date "2006-06-01" @default.
- W2150008165 modified "2023-10-05" @default.
- W2150008165 title "Augmenting forests to meet odd diameter requirements" @default.
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- W2150008165 doi "https://doi.org/10.1016/j.disopt.2005.10.006" @default.
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