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Lea-TN: leader election algorithm considering node and link failures in a torus network

The Journal of Supercomputing volume 77, pages 13292–13329 (2021)Cite this article

Abstract

Torus network topology offers many advantages such as higher speed, lower latency, better fairness, and lower energy consumption. For these kinds of benefits, nowadays, it is used to construct many parallel and distributed systems like IBM Blue Gene, IBM Sequoia, Mira, and Sugon TC8600. In parallel and distributed computing, multiple nodes act together to carry out large tasks fast. Hence, coordination is indispensable among these nodes to complete such tasks. A possible coordination method could be to elect a leader among the nodes. Along with coordination, the elected leader node also manages other activities such as task allocation, result aggregation, clock synchronization, proficient resource sharing management, and communication among the system’s nodes. In this paper, we propose a lower bound \(\varOmega (N\log _3 N)\) of message complexity on a comparison-based leader election for a 2D torus network (where N is the number of nodes in the network). Next, we sketch a new leader election algorithm (Lea-TN) considering both the node and link failures for a 2D torus network. This Lea-TN is a deterministic and robust algorithm that elects a leader for a synchronous distributed system. The algorithm chooses a leader, even when there are some link or node failures in the system. We consider the number of non-faulty links and the subsisting nodes’ failure rate to elect a reliable leader. We introduce new patterns for sending messages that help reduce the number of exchanged messages and the execution time of the election process. The proposed algorithm (Lea-TN) enables a node to identify its link failures during the election also. Further, we simulate the Lea-TN algorithm and compare its performance with that of the well-known existing algorithms.

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Notes

  1. In the next sections, “Leader Election Algorithm in 2D Torus Networks with the Presence of One Link Failure” is represented as “LEA with One Link Failure.”

  2. In the next sections, “Dynamic Leader Election Algorithm in 2D Torus Network with Multi Links Failure” is represented as “Dynamic LEA with Multi Links Failure.”

References

  1. Abraham I, Dolev D, Halpern JY (2019) Distributed protocols for leader election: a game-theoretic perspective. ACM Trans Econ Comput (TEAC) 7(1):1–26

    MathSciNet  Article  Google Scholar 

  2. Abu-Amara HH (1988) Fault-tolerant distributed algorithm for election in complete networks. IEEE Trans Comput 37(4):449–453

    Article  Google Scholar 

  3. Al Refai M (2014) Dynamic leader election algorithm in 2d torus network with multi links failure. IJCST 2(5):150–156

    Google Scholar 

  4. Altisen K, Datta AK, Devismes S, Durand A, Larmore LL (2016) Leader election in rings with bounded multiplicity (short paper). In: International Symposium on Stabilization, Safety, and Security of Distributed Systems. Springer, pp 1–6

  5. Antonoiu G, Srimani PK (1996) A self-stabilizing leader election algorithm for tree graphs. J Parallel Distrib Comput 34(2):227–232

    Article  Google Scholar 

  6. Attiya H, Welch J (2004) Distributed computing: fundamentals, simulations, and advanced topics, vol 19. Wiley

  7. Balakrishnan N (2007) The Weibull analysis handbook. J Qual Technol 39(1):85

    Article  Google Scholar 

  8. van Baronaigien DR (2000) Loop free generation of k-ary trees. Am J Math Manag Sci 20(1–2):183–200

    MathSciNet  MATH  Google Scholar 

  9. Birkur SK (2012) Link failure detector and simulation of metrics in distributed network. Ph.D. thesis, Texas A&M University-Corpus Christi

  10. Biswas A, Dutta A (2016) A timer based leader election algorithm. In: Ubiquitous intelligence & computing, advanced and trusted computing, scalable computing and communications, cloud and big data computing, internet of people, and smart world congress (UIC/ATC/ScalCom/CBDCom/IoP/SmartWorld), 2016 Intl IEEE Conferences. IEEE, pp 432–439

  11. Biswas A, Maurya AK, Tripathi AK, Aknine S (2020) Frlle: a failure rate and load based leader election algorithm for a bidirectional ring in distributed systems. J Supercomput

  12. Burns JE (1980) A formal model for message-passing systems. Technical Report 91

  13. Cachin C, Guerraoui R, Rodrigues L (2011) Introduction to reliable and secure distributed programming. Springer

  14. Camara JM, Moreto M, Vallejo E, Beivide R, Miguel-Alonso J, Martinez C, Navaridas J (2010) Twisted torus topologies for enhanced interconnection networks. IEEE Trans Parallel Distrib Syst 21(12):1765–1778

    Article  Google Scholar 

  15. Chandra TD, Toueg S (1996) Unreliable failure detectors for reliable distributed systems. J ACM (JACM) 43(2):225–267

    MathSciNet  Article  Google Scholar 

  16. Chang E, Roberts R (1979) An improved algorithm for decentralized extrema-finding in circular configurations of processes. Commun ACM 22(5):281–283

    Article  Google Scholar 

  17. Chatterjee S, Pandurangan G, Robinson P (2019) The complexity of leader election in diameter-two networks. Distrib Comput pp 1–17

  18. Dagdeviren O, Erciyes K (2008) A hierarchical leader election protocol for mobile ad hoc networks. In: International Conference on Computational Science. Springer, pp 509–518

  19. DeCleene B, Dondeti L, Griffin S, Hardjono T, Kiwior D, Kurose J, Towsley D, Vasudevan S, Zhang C (2001) Secure group communications for wireless networks. In: 2001 MILCOM proceedings communications for network-centric operations: creating the information force (Cat. No. 01CH37277). IEEE, vol 1, pp 113–117

  20. Essinger S, Zhu X, Schnee M, Liu J, Shen X, Chen L, Lu J (2013) Wireless dual-function network device dynamically switching and reconfiguring from a wireless network router state of operation into a wireless network coordinator state of operation in a wireless communication network. US Patent 8,457,013

  21. Fich F, Ruppert E (2000) Lower bounds in distributed computing. In: International Symposium on Distributed Computing. Springer, pp 1–28

  22. Fujimoto RM (2000) Parallel and distributed simulation systems, vol 300. Wiley, New York

    Google Scholar 

  23. Fussell J (1975) How to hand-calculate system reliability and safety characteristics. IEEE Trans Reliab 24(3):169–174

    Article  Google Scholar 

  24. Garcia-Molina H (1982) Elections in a distributed computing system. IEEE Trans Comput 31(1):48–59

    Article  Google Scholar 

  25. Gusella R, Zatti S (1989) The accuracy of the clock synchronization achieved by tempo in Berkeley unix 4.3 bsd. IEEE Trans Softw Eng 15(7):847–853

    Article  Google Scholar 

  26. Hatzis KP, Pentaris GP, Spirakis PG, Tampakas VT, Tan RB (1999) Fundamental control algorithms in mobile networks. In: Proceedings of the Eleventh Annual ACM Symposium on Parallel Algorithms and Architectures, pp 251–260

  27. Hirschberg DS, Sinclair JB (1980) Decentralized extrema-finding in circular configurations of processors. Commun ACM 23(11):627–628

    MathSciNet  Article  Google Scholar 

  28. Kordafshari M, Gholipour M, Mosakhani M, Haghighat A, Dehghan M (2005) Modified bully election algorithm in distributed systems. WSEAS Trans Inf Sci Appl 2(8):1189–1194

    Google Scholar 

  29. Korsh JF (1994) Loopless generation of k-ary tree sequences. Inf Process Lett 52(5):243–247

    MathSciNet  Article  Google Scholar 

  30. Le Lann G (1977) Distributed systems-towards a formal approach. IFIP Congress, Toronto 7:155–160

    Google Scholar 

  31. Loui MC (1984) The complexity of sorting on distributed systems. Inf Control 60(1–3):70–85

    MathSciNet  Article  Google Scholar 

  32. Malpani N, Welch JL, Vaidya N (2000) Leader election algorithms for mobile ad hoc networks. In: Proceedings of the 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications. ACM, pp 96–103

  33. Mashreghi A, King V (2018) Broadcast and minimum spanning tree with \( o (m) \) messages in the asynchronous congest model. arXiv preprint arXiv:180604328

  34. Modarres M, Kaminskiy MP, Krivtsov V (2016) Reliability engineering and risk analysis: a practical guide. CRC Press

  35. Owicki S, Lamport L (1982) Proving liveness properties of concurrent programs. ACM Trans Program Lang Syst (TOPLAS) 4(3):455–495

    Article  Google Scholar 

  36. Perkins CE, Royer EM (1999) Ad-hoc on-demand distance vector routing. Proceedings WMCSA’99. Second IEEE Workshop on Mobile Computing Systems and Applications. IEEE, pp 90–100

  37. Raychoudhury V, Cao J, Niyogi R, Wu W, Lai Y (2014) Top k-leader election in mobile ad hoc networks. Pervasive Mob Comput 13:181–202

    Article  Google Scholar 

  38. Raynal M (2013) Distributed algorithms for message-passing systems, vol 500. Springer

  39. Refai M (2015) Leader election algorithms in torus and hypercube networks comparisons and survey. Int J Comput Sci Mob Comput (IJCSMC) 4(1):102–111

    MathSciNet  Google Scholar 

  40. Refai M, Sharieh A, Alshammari F (2010) Leader election algorithm in 2d torus networks with the presence of one link failure. Int Arab J Inf Technol 7(2):105–114

    Google Scholar 

  41. Rinne H (2008) The Weibull distribution: a handbook. Chapman and Hall/CRC

  42. Singh G (1996) Leader election in the presence of link failures. IEEE Trans Parallel Distrib Syst 7(3):231–236

    Article  Google Scholar 

  43. Sudo Y, Ooshita F, Kakugawa H, Masuzawa T, Datta AK, Larmore LL (2018) Loosely-stabilizing leader election for arbitrary graphs in population protocol model. IEEE Trans Parallel Distrib Syst 30(6):1359–1373

    Article  Google Scholar 

  44. Tanenbaum AS, Van Steen M (2007) Distributed systems: principles and paradigms. Prentice-Hall

  45. Ulug ME (1988) Method and apparatus for maintaining a dynamic logical ring in a token passing lan. US Patent 4,745,598

  46. Villadangos J, Cordoba A, Fariña F, Prieto M (2005) Efficient leader election in complete networks. In: Parallel, distributed and network-based processing, 2005. PDP 2005. 13th Euromicro Conference on. IEEE, pp 136–143

  47. Yifrach A, Mansour Y (2018) Fair leader election for rational agents in asynchronous rings and networks. In: Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing. ACM, pp 217–226

  48. Yu K, Gao M, Jiang H, Li G (2017) Multi-leader election in dynamic sensor networks. EURASIP J Wireless Commun Netw 1:187

    Article  Google Scholar 

  49. Zomaya AY et al (1996) Parallel and distributed computing handbook. McGraw-Hill, New York

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology (BHU), Varanasi, India

    Amit Biswas & Anil Kumar Tripathi

  2. LIRIS Laboratory Université Claude Bernard Lyon 1, Lyon1, France

    Samir Aknine

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  1. Amit Biswas
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  2. Anil Kumar Tripathi
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  3. Samir Aknine
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Biswas, A., Tripathi, A.K. & Aknine, S. Lea-TN: leader election algorithm considering node and link failures in a torus network. J Supercomput 77, 13292–13329 (2021). https://doi.org/10.1007/s11227-021-03803-7

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Keywords

  • Leader election
  • Distributed computing
  • Network topology
  • Lower bound
  • Failure rate
  • Complexity analysis