An instance of the non-preemptive tree packing problem consists of an undirected graph $G=(V,E)$ together with a weight $w(e)$ for every edge $e\in E$. The goal is to activate every edge $e$ for some time interval of length $w(e)$, such that the activated edges keep $G$ connected for the longest possible overall time.

We derive a variety of results on this problem. The problem is strongly NP-hard even on graphs of treewidth~$2$, and it does not allow a polynomial time approximation scheme (unless P=NP). Furthermore, we discuss the performance of a simple greedy algorithm, and we construct and analyze a number of parametrized and exact algorithms.

https://link.springer.com/chapter/10.1007/978-3-030-79987-8_32