Improving the stretch factor of a geometric network by edge augmentation

M. Farshi, P. Giannopoulos, J. Gudmundsson

Research output: Contribution to journalArticleAcademicpeer-review

25 Citations (Scopus)
114 Downloads (Pure)

Abstract

Given a Euclidean graph $G$ in $\mathbb{R}^d$ with $n$ vertices and $m$ edges, we consider the problem of adding an edge to $G$ such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a graph with positive edge weights runs in $\cal{O}$$(nm+n^2 \log n)$ time, resulting in a trivial $\cal{O}$$(n^3m+n^4 \log n)$-time algorithm for computing the optimal edge. First, we show that a simple modification yields the optimal solution in $\cal{O}$$(n^4)$ time using $\cal{O}$$(n^2)$ space. To reduce the running time we consider several approximation algorithms.
Original languageEnglish
Pages (from-to)226-240
JournalSIAM Journal on Computing
Volume38
Issue number1
DOIs
Publication statusPublished - 2008

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