An Improved Algorithm for Diameter-Optimally Augmenting Paths in a Metric Space
August 16, 2016 Β· Declared Dead Β· π Workshop on Algorithms and Data Structures
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Authors
Haitao Wang
arXiv ID
1608.04456
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.CG
Citations
11
Venue
Workshop on Algorithms and Data Structures
Last Checked
4 months ago
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 observations and different algorithmic techniques, we present an $O(n\log n)$ time algorithm.
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