The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Cancellation in cyclic consecutive systems
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
On the characterization of the domination of a diameter-constrained network reliability model
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
New reliability model and its application to assess the performance of sensor networks
MMES'10 Proceedings of the 2010 international conference on Mathematical models for engineering science
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The domination invariant has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. Previous papers have explored the relation between undirected network systems and matroids. In this paper the main focus is on directed network systems and their relation to oriented matroids. An oriented matroid is a special type of matroid where the circuits are signed sets. Using these signed sets one can e.g., obtain a set theoretic representation of the direction of the edges of a directed network system. Classical results for directed network systems include the fact that the signed domination is either +1 or -1 if the network is acyclic, and zero otherwise. It turns out that these results can be generalized to systems derived from oriented matroids. Several classes of systems for which the generalized results hold will be discussed. These include oriented versions of k-out-of-n systems and a certain class of systems associated with matrices.