Incremental Network Design with Minimum Spanning Trees

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.Comment: 9 pages, minor revision based on reviewer comment

Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph G = (V,E) and a set E0⊂E , the incremental network design problem with minimum spanning trees asks for a sequence of edges e′ 1 , … , e ′ T ∈ E ∖ E 0 minimizing ∑ T t = 1 w ( X t ) where w(Xt) is the weight of a minimum spanning tree Xt for the subgraph (V,E0∪ { e ′ 1 , … , e ′ T } ) and T=|E∖ E 0 |. We prove that this problem can be solved by a greedy algorithm