Incremental Network Design with Minimum Spanning Trees

TL;DR

This paper studies an incremental network design problem where edges are added to maintain minimum spanning trees, and proves that a greedy algorithm can optimally solve this problem.

Contribution

It demonstrates that the incremental network design problem with minimum spanning trees can be efficiently solved using a greedy algorithm, providing a new approach for dynamic network optimization.

Findings

The greedy algorithm finds an optimal solution for the incremental network design problem.

The problem can be efficiently solved without complex optimization techniques.

This approach simplifies dynamic network design with minimum spanning trees.

Abstract

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.