On a directed tree problem motivated by a newly introduced graph product

Abstract

In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic real-time processes. While the two conference papers were focussing more on the applications, here we mainly deal with the graph theoretical and computational complexity issues. We show that the directed tree problem is NP-complete and present and compare several heuristics for this problem.

Keywords

• finite deterministic directed acyclic labelled multi-graphs, vertex removing synchronised graph product, target trees, periodic real-time systems