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LP-Based Algorithms for Computing Maximum Vertex-Disjoint Paths with Different Colors

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Theory and Applications of Models of Computation (TAMC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12337))

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Abstract

Booming applications in wireless networks have imposed a great growth in data transmission together with stricter requirements of bandwidth and load balancing. In order to capture and meet the requirements, we consider a new problem of computing maximum disjoint paths with different colors (MDPDC) in networks. In MDPDC, transmission frequencies are modeled as different colors and the aim is to find a maximum number of constrained node-disjoint paths where nodes in any disjoint path share the same color, while colors are different among paths. Observing the \(\mathcal{NP}\)-completeness of MDPDC, the paper proposes two linear programming based algorithms as generic solutions.

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References

  1. https://standards.ieee.org/standard/802_1D-2004.html

  2. Bonizzoni, P., Dondi, R., Pirola, Y.: Maximum disjoint paths on edge-colored graphs: approximability and tractability. Algorithms 6(1), 1–11 (2013)

    Article  MathSciNet  Google Scholar 

  3. Challal, Y., Ouadjaout, A., Lasla, N., Bagaa, M., Hadjidj, A.: Secure and efficient disjoint multipath construction for fault tolerant routing in wireless sensor networks. J. Netw. Comput. Appl. 34(4), 1380–1397 (2011)

    Article  Google Scholar 

  4. Chekuri, C., Khanna, S., Shepherd, F.B.: The all-or-nothing multicommodity flow problem. In: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing, pp. 156–165. ACM (2004)

    Google Scholar 

  5. Chekuri, C., Khanna, S., Shepherd, F.B.: Multicommodity flow, well-linked terminals, and routing problems. In: Proceedings of the Thirty-seventh Annual ACM Symposium on Theory of Computing, pp. 183–192. ACM (2005)

    Google Scholar 

  6. Deng, Y., Guo, L., Huang, P.: Exact algorithms for finding partial edge-disjoint paths. In: Wang, L., Zhu, D. (eds.) COCOON 2018. LNCS, vol. 10976, pp. 14–25. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94776-1_2

    Chapter  Google Scholar 

  7. Dondi, R., Sikora, F.: Finding disjoint paths on edge-colored graphs: more tractability results. J. Comb. Optim. 36(4), 1315–1332 (2017). https://doi.org/10.1007/s10878-017-0238-6

    Article  MathSciNet  MATH  Google Scholar 

  8. Fortune, S., Hopcroft, J., Wyllie, J.: The directed subgraph homeomorphism problem. Theoret. Comput. Sci. 10(2), 111–121 (1980)

    Article  MathSciNet  Google Scholar 

  9. Frank, A.: Edge-disjoint paths in planar graphs. J. Comb. Theory Ser. B 39(2), 164–178 (1985)

    Article  MathSciNet  Google Scholar 

  10. Guo, L., Deng, Y., Liao, K., He, Q., Sellis, T., Hu, Z.: A fast algorithm for optimally finding partially disjoint shortest paths. In: IJCAI, pp. 1456–1462 (2018)

    Google Scholar 

  11. Hou, A., Wu, C.Q., Fang, D., Wang, Y., Wang, M.: Bandwidth scheduling for big data transfer using multiple fixed node-disjoint paths. J. Network Comput. Appl. 85, 47–55 (2017)

    Article  Google Scholar 

  12. Kawarabayashi, K.I., Kobayashi, Y.: All-or-nothing multicommodity flow problem with bounded fractionality in planar graphs. In: IEEE Symposium on Foundations of Computer Science (2013)

    Google Scholar 

  13. Lin, G., Soh, S., Chin, K.-W., Lazarescu, M.: Energy aware two disjoint paths routing. J. Netw. Comput. Appl. 43, 27–41 (2014)

    Article  Google Scholar 

  14. Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B 63, 65–110 (1995)

    Article  MathSciNet  Google Scholar 

  15. Schrijver, A.: Finding k disjoint paths in a directed planar graph. SIAM J. Comput. 23(4), 780–788 (1994)

    Article  MathSciNet  Google Scholar 

  16. Shiloach, Y.: A polynomial solution to the undirected two paths problem. J. the ACM (JACM) 27(3), 445–456 (1980)

    Article  MathSciNet  Google Scholar 

  17. Tholey, T.: Solving the 2-disjoint paths problem in nearly linear time. Theory Comput. Syst. 39(1), 51–78 (2006)

    Article  MathSciNet  Google Scholar 

  18. Wu, B.Y.: On the maximum disjoint paths problem on edge-colored graphs. Discrete Optim. 9(1), 50–57 (2012)

    Article  MathSciNet  Google Scholar 

  19. Yallouz, J., Rottenstreich, O., Babarczi, P., Mendelson, A., Orda., A.: Optimal link-disjoint node-“somewhat disjoint" paths. In: 2016 IEEE 24th International Conference on Network Protocols (ICNP), pp. 1–10. IEEE (2016)

    Google Scholar 

  20. Zhang, S., Chen, L., Yang, W.: On fault-tolerant path optimization under QoS constraint in multi-channel wireless networks. Theoret. Comput. Sci. 695, 74–82 (2017)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by Natural Science Foundation of China (No. 61772005) and Natural Science Foundation of Fujian Province (No. 2017J01753). Part of the research was done when the first and forth authors were with College of Mathematics and Computer Science, Fuzhou University, P.R. China.

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Authors and Affiliations

  1. Officers College of Chinese People’s Armed Police Force, Chengdu, 610213, People’s Republic of China

    Yunyun Deng

  2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, People’s Republic of China

    Yi Chen

  3. Peter Faber Business School, Australian Catholic University, Sydney, Australia

    Kewen Liao

  4. School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, People’s Republic of China

    Longkun Guo

Authors
  1. Yunyun Deng
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  2. Yi Chen
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  3. Kewen Liao
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  4. Longkun Guo
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Corresponding author

Correspondence to Longkun Guo .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, USA

    Jianer Chen

  2. School of Computer Science and Engineering, Central South University, Changsha, China

    Qilong Feng

  3. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, USA

    Jinhui Xu

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Deng, Y., Chen, Y., Liao, K., Guo, L. (2020). LP-Based Algorithms for Computing Maximum Vertex-Disjoint Paths with Different Colors. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_10

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  • DOI: https://doi.org/10.1007/978-3-030-59267-7_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59266-0

  • Online ISBN: 978-3-030-59267-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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