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Routing and wavelength assignment for exchanged crossed cubes on ring-topology optical networks

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Abstract

The exchanged crossed cube, denoted by \(\textit{ECQ}(s, t)\), is a novel graph with fewer edges and smaller diameter compared to other variations of the corresponding hypercube. The ring topology, denoted by \(R_n\), is one of the most popular topologies in Wavelength division multiplexing optical networks. This paper addresses the routing and wavelength assignment problem for realizing \(\textit{ECQ}(s, t)\) communication pattern on \(R_n\), where \(n=s+t+1\). We propose an embedding scheme. Base on the embedding scheme, a wavelength assignment algorithm using \(2^{s+t-2}+\lfloor 2^t/3\rfloor \) wavelengths is devised. We show that the wavelength assignment algorithm uses no more than 1.25 times of wavelengths compared to the optimal wavelength number, i.e., it is a factor 1.25 approximation algorithm. Moreover, the number of additional required wavelengths is no more than \(\lfloor 2^{t-1}/3\rfloor \).

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, Aletheia University, New Taipei City, 25103, Taiwan

    Yu-Liang Liu

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Correspondence to Yu-Liang Liu.

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Communicated by G. Yi.

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Liu, YL. Routing and wavelength assignment for exchanged crossed cubes on ring-topology optical networks. Soft Comput 22, 6693–6703 (2018). https://doi.org/10.1007/s00500-018-3071-7

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