Abstract
Let P be a path graph of n vertices embedded in a metric space. We consider the problem of adding a new edge to P such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in \(O(n\log ^3 n)\) time. In this paper, based on new algorithmic techniques and observations, we present an \(O(n\log n)\) time algorithm.
This research was supported in part by NSF under Grant CCF-1317143.
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Wang, H. (2017). An Improved Algorithm for Diameter-Optimally Augmenting Paths in a Metric Space. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_46
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DOI: https://doi.org/10.1007/978-3-319-62127-2_46
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