Non-Preemptive Tree Packing

Algorithmica, vol. 85, pp. 783–804

Abstract

Abstract An instance of the non-preemptive tree packing problem consists of an undirected graph $$G=(V,E)$$ G = ( V , E ) together with a weight w(e) for every edge $$e\in E$$ 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.

Authors 3

1. Stefan Lendl

   University of Graz

   Affiliation as printed

   Department of Operations and Information Systems, University of Graz, Graz, Styria Austria

   Department of Operations and Information Systems, University of Graz, Graz, Styria, Austria

2. Gerhard J. Woeginger Aachen Department of Computer Science

   RWTH Aachen University

   Affiliation as printed

   Department of Computer Science, RWTH Aachen, Aachen, North Rhine-Westphalia Germany

   Department of Computer Science, RWTH Aachen, Aachen, North Rhine-Westphalia, Germany

3. Lasse Wulf corresponding

   Graz University of Technology

   Affiliation as printed

   Institute of Discrete Mathematics, Graz University of Technology, Graz, Styria Austria

   Institute of Discrete Mathematics, Graz University of Technology, Graz, Styria, Austria