Skip to main content
Log in

Application of acyclic coloring in wavelength assignment problem for butterfly and Beneš network

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

The routing and wavelength assignment problem is crucial because it increases the efficiency of wavelength-routed all-optical networks built on the Wavelength Division Multiplexing approach. Given the physical network topology, the problem aims to establish routes for the connection requests and assign to each of them, a wavelength in accordance with the wavelength continuity and distinct wavelength constraints. In order to fulfill all requests, it is important to use the fewest possible wavelengths. This work proposes a novel method for determining the wavelength by employing acyclic coloring to determine the routing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Settembre M and Matera F 1993 All-optical implementations for high-capacity TDMA networks. Fiber Integr. Opt. 12: 173–186

    Article  Google Scholar 

  2. Zang H, Jue J P and Mukherjee B 2000 A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks. Optical Networks Magazine. 1: 47–60

    Google Scholar 

  3. Gerstel O and Kutten S 1997 Dynamic wavelength allocation in all-optical ring networks. Proc., IEEE ICC ’97. 1: 432–436

    Google Scholar 

  4. Murthy C S R and Gurusamy M 2002 WDM optical networks: concepts, design, and algorithm. Prentice Hall

    Google Scholar 

  5. Chen Y and Shen H 2010 Routing and wavelength assignment for hypercube in array-based WDM optical networks. J. Parallel Distrib. Comput. 70: 59–68

    Article  MATH  Google Scholar 

  6. Liu Y L 2015 Routing and wavelength assignment for exchanged hypercubes in linear array optical networks. Inf. Process. Lett. 115: 203–208

    Article  MathSciNet  MATH  Google Scholar 

  7. Liu Y L 2018 Routing and wavelength assignment for exchanged crossed cubes on ring-topology optical networks. Soft Comput. 22: 6693–6703

    Article  MATH  Google Scholar 

  8. Li T K, Chien M J, Chen J C and Tsai C H 2018 Routing and wavelength assignment for augmented cubes in array-based wavelength-division-multiplexing optical networks. Int. J. Comput. Math.: Comput. Syst. Theory. 3: 92–105

    MathSciNet  Google Scholar 

  9. Liu Y L 2022 Routing and Wavelength Allotment for Exchanged Folded Hypercube Communications Embedded in Bus-Topology WDM Optical Networks. Mobile Networks and Appl. 27: 109–117

    Article  Google Scholar 

  10. Grünbaum B 1973 Acyclic colorings of planar graphs. Isr. J. Math. 14: 390–408

    Article  MathSciNet  MATH  Google Scholar 

  11. Fiamčik J 1978 The acyclic chromatic class of a graph. Math. Slovaca. 28: 139–145

    MathSciNet  MATH  Google Scholar 

  12. Alon N and Zaks A 2002 Algorithmic aspects of acyclic edge colorings. Algorithmica 32: 611–614

    Article  MathSciNet  MATH  Google Scholar 

  13. Alt H, Fuchs U and Kriegel K 1999 On the number of simple cycles in planar graphs. Comb. Probab. Comput. 8: 397–405

    Article  MathSciNet  MATH  Google Scholar 

  14. Kostochka A V 1978 Upper bounds of chromatic functions of graphs. In Doct. Thesis. Novosibirsk, Russia

  15. Gebremedhin A H, Tarafdar A, Manne F and Pothen A 2007 New Acyclic and Star Coloring Algorithms with Application to Computing Hessians. SIAM J. Sci. Comput. 29: 1042–1072

    Article  MathSciNet  MATH  Google Scholar 

  16. Amar D, Raspaud A and Togni O 2001 All-to-all wavelength-routing in all-optical compound networks. Discrete Math. 235: 353–363

    Article  MathSciNet  MATH  Google Scholar 

  17. Balaban A T 1985 Applications of graph theory in chemistry. J. Chem. Inf. Comput. Sci. 25: 334–343

    Article  Google Scholar 

  18. Graver J E and Hartung E J 2014 Kekuléan benzenoids. J. Math. Chem. 52: 977–989

    Article  MathSciNet  MATH  Google Scholar 

  19. Moffatt I 2011 Unsigned state models for the jones polynomial. Ann. Comb. 15: 127–146

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhang W 2022 Local conditions for planar graphs of acyclic edge coloring. J. Appl. Math. Comput. 68: 721–738

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang J, Miao L, Song W and Liu Y 2021 Acyclic Coloring of Graphs with Maximum Degree 7. Graphs Comb. 37: 455–469

    Article  MathSciNet  MATH  Google Scholar 

  22. Ma Y, Shi Y and Wang W 2021 Acyclic Edge Coloring of Chordal Graphs with Bounded Degree. Graphs Comb. 37: 2621–2636

    Article  MathSciNet  MATH  Google Scholar 

  23. Fialho P M, de Lima B N and Procacci A 2020 A new bound on the acyclic edge chromatic number. Discrete Math. 343: 112037

    Article  MathSciNet  MATH  Google Scholar 

  24. Song W Y, Duan Y Y, Wang J and Miao L Y 2020 Acyclic Edge Coloring of IC-planar Graphs. Acta Math. Appl. Sin., English Series. 36: 581–589

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang J and Miao L 2019 Acyclic coloring of graphs with maximum degree at most six. Discrete Math. 342: 3025–3033

    Article  MathSciNet  MATH  Google Scholar 

  26. Beineke L W and Wilson R J 1973 On the edge-chromatic number of a graph. Discrete Math. 5: 15–20

    Article  MathSciNet  MATH  Google Scholar 

  27. Hudák D, Kardoš F, Lužar B, Soták R and Škrekovski R 2012 Acyclic edge coloring of planar graphs with \(\Delta \) colors. Discrete Appl. Math. 160: 1356–1368

    Article  MathSciNet  MATH  Google Scholar 

  28. Xu J M 2001 Topological Structure and Analysis of Interconnection Networks. Kluwer Academic Publishers

    Book  MATH  Google Scholar 

  29. Zhang J, Yang X, Yu C and He L 2015 Dynamic wavelength assignment for realizing hypercube-based bitonic sorting on wavelength division multiplexing linear arrays. Int. J. Comput. Math. 92: 218–229

    Article  MathSciNet  MATH  Google Scholar 

  30. Chen Y, Shen H and Liu F 2006 Wavelength assignment for realizing parallel FFT on regular optical networks. J. Supercomput. 36: 3–16

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A Berin Greeni.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Navis, V.V., Greeni, A.B. Application of acyclic coloring in wavelength assignment problem for butterfly and Beneš network. Sādhanā 48, 146 (2023). https://doi.org/10.1007/s12046-023-02164-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-023-02164-6

Keywords

Navigation