Geodesic
Incremental Network Design with Minimum Spanning Trees
Journal of Graph Algorithms and Applications, Tome 21 (2017) no. 4, pp. 417-432.

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Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.
DOI : 10.7155/jgaa.00423
Keywords: network design, scheduling, greedy algorithm, matroid, minimum spanning tree 
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Konrad Engel; Thomas Kalinowski; Martin Savelsbergh. Incremental Network Design with Minimum Spanning Trees. Journal of Graph Algorithms and Applications, Tome 21 (2017) no. 4, pp. 417-432. doi : 10.7155/jgaa.00423. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00423/

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