Decompositions of graphs based on a new graph product

Recently, we have introduced a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP) is based on modifications of the well-known Cartesian product, and closely related to the synchronised product due to Wöhrle and Thomas. Here, we recall the definition of the VRSP and use it to define two different decompositions of graphs. Although our main results apply to directed labelled acyclic multigraphs, the VRSP can also be used to decompose any undirected graph of order at least 4 into two smaller graphs

Improving the performance of periodic real-time processes: a graph theoretical approach

In this paper the performance gain obtained by combining parallel periodic real-time processes is elaborated. In certain single-core mono-processor configurations, for example embedded control systems in robotics comprising many short processes, process context switches may consume a considerable amount of the available processing power. For this reason it can be advantageous to combine processes, to reduce the number of context switches and thereby increase the performance of the application. As we consider robotic applications only, often consisting of processes with identical periods, release times and deadlines, we restrict these configurations to periodic real-time processes executing on a single-core mono-processor. By graph theoretical concepts and means, we provide necessary and sufficient conditions so that the number of context switches can be reduced by combining synchronising processes

On a Directed Tree Problem Motivated by a Newly Introduced Graph Product

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