Non-Preemptive Tree Packing.

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 ∈ 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 parameterized and exact algorithms.