An Improved Algorithm for Diameter-Optimally Augmenting Paths in a Metric Space

August 16, 2016 Β· Declared Dead Β· πŸ› 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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