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WDM/OFDM-networks: Transformations, embeddings, and dualism

: Giglmayr, J.


Cryan, R.A. ; Society of Photo-Optical Instrumentation Engineers -SPIE-, Bellingham/Wash.:
All-Optical Communication Systems: Architecture, Control, and Network Issues II : 20 - 21 November 1996, Boston, Massachusetts
Bellingham/Wash.: SPIE, 1996 (SPIE Proceedings Series 2919)
ISBN: 0-8194-2321-1
Conference "All-Optical Communication Systems: Architecture, Control, and Network Issues" <2, 1996, Boston/Mass.>
Fraunhofer HHI ()
duality (mathematics); frequency division multiplexing; graph theory; network topology; optical fibre networks; optimisation; wavelength division multiplexing; wdm/ofdm-networks; transformations; embeddings; dualism; multigraphs; graph models; optimization; multiple edges; planar graphs; hypergraphs; nonregular simple graphs/networks

The WDM/OFDM-networks of the paper are multigraphs (several edges/wavelengths between two nodes). Transformations of these graph models are presented and applied to WDM/OFDM-networks for their later analysis and optimization. The paper concentrates on two transformations, the complement and the dual of WDM/OFDM-networks. However, the complement exists only for simple graphs (one edge between two nodes) whereas WDM/OFDM-networks are multigraphs with multiple edges between two nodes. The computation of the dual is simple only for planar graphs (no crossings) and for regular graphs in terms of hypergraphs (more than two nodes are related to each edge). Throughout the paper, the dual and the complement of nonregular simple graphs/networks are computed by means of computer programs. However, the aim of the ongoing work is to compute the dual and the complement of multigraphs. By means of the dual of multigraphs the topologically equivalent ( identical to isomorphic) simple graph (one wavelength) and in turn the complement may be obtained which both are aimed to extend the range of analysis and design concepts of WDM/OFDM-networks. Various examples are presented which explain the applied concepts.