Optical Routing of Uniform Instances in Tori

  • Francesc Comellas
  • Margarida Mitjana
  • Lata Narayanan
  • Jaroslav Opatrny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)


We consider the problem of routing uniform communication instances in switched optical tori that use the wavelength division multplexing (or WDM) approach. A communication instance is called uniform if it consists exactly of all pairs of nodes in the graph whose distance is equal to one from a specified set S = d 1; d2;...; d k. We give bounds on the optimal load induced on an edge for any uniform instance in a torus Tnxn. When k = 1, we prove necessary and sufficient conditions on the value in S relative to n for the wavelength index to be equal to the load. When k≥ 2, we show that for any set S, there exists an n0, such that for all n > n0, there is an optimal wavelength assignment for the communication instance specified by S on the torus Tnxn. We also show an approximation for the wavelength index for any S and n. Finally, we give some results for rectangular tori.


Optical Network Vertical Edge Horizontal Edge Wavelength Assignment Communication Instance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Francesc Comellas
    • 1
  • Margarida Mitjana
    • 2
  • Lata Narayanan
    • 3
  • Jaroslav Opatrny
    • 3
  1. 1.Departament de Matemática Aplicada i TelematicaUniversitat Politécnica de CatalunyaBarcelonaSpain
  2. 2.Departament de Matemática Aplicada IUniversitat Politécnica de CatalunyaBarcelonaSpain
  3. 3.Department of Computer ScienceConcordia UniversityMontrealCanada

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