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Distributed and incremental travelling salesman algorithm on time-evolving graphs

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Abstract

Travelling salesman problem (TSP) is a graph problem that has been widely used in many applications, especially for transportation and logistics. Because TSP is a NP hard problem, minimizing the complexity of TSP algorithms is an important problem. Many heuristic algorithms have been proposed to compute the TSP tours of a given static graph. But limited studies have been done on time-evolving graph (TEG) where the graph can change over time due to update events, such as weight changes on edges or vertices. It is a more challenging problem because the speed of TSP computations must be high enough to catch up the graph update frequency. In this paper, we make the very first attempt to minimize the computation time of solving TSP on time-evolving graphs. By exploring parallel computing power and reusing previous computing results, we proposed a distributed and incremental TSP algorithm which can be implemented on vertex-centric parallel graph computing frameworks to efficiently find TSP tours on large changing graphs. Our incremental algorithm can maintain shortest TSP tour with minimum amount of recomputation. Through our experimental evaluation, we have shown incremental TSP algorithm is 98% faster than distributed algorithm.

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References

  1. Abdolrashidi A, Ramaswamy L (2016) Continual and cost-effective partitioning of dynamic graphs for optimizing big graph processing systems. In: 2016 IEEE International Congress on Big Data (BigData Congress), pp. 18–25 . https://doi.org/10.1109/BigDataCongress.2016.12

  2. Anagnostopoulos A, Kumar R, Mahdian M, Upfal E, Vandin F (2012) Algorithms on evolving graphs. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS ’12, pp. 149–160. ACM, New York, NY, USA . https://doi.org/10.1145/2090236.2090249

  3. Bahmani B, Kumar R, Mahdian M, Upfal E (2012) Pagerank on an evolving graph. In: Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’12, pp. 24–32. ACM, New York, NY, USA . https://doi.org/10.1145/2339530.2339539

  4. Blelloch GE, Gu Y, Shun J, Sun Y (2020) Randomized incremental convex hull is highly parallel. In: Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA ’20, p. 103–115. Association for Computing Machinery, New York, NY, USA . https://doi.org/10.1145/3350755.3400255

  5. Brighen A, Slimani H, Rezgui A, Kheddouci H (2019) Listing all maximal cliques in large graphs on vertex-centric model. J. Supercomput. 75(8), 4918–4946 . http://dblp.uni-trier.de/db/journals/tjs/tjs75.html#BrighenSRK19

  6. Chen P (2013) An improved genetic algorithm for solving the traveling salesman problem. In: 2013 Ninth International Conference on Natural Computation (ICNC), pp. 397–401 . https://doi.org/10.1109/ICNC.2013.6818008

  7. Chen Z, Shen HT, Zhou X, Yu JX (2009) Monitoring path nearest neighbor in road networks. In: Proceedings of the 2009 ACM SIGMOD International Conference on Management of Data, SIGMOD ’09, pp. 591–602

  8. Cheng R, Hong J, Kyrola A, Miao Y, Weng X, Wu M, Yang F, Zhou L, Zhao F, Chen E (2012) Kineograph: Taking the pulse of a fast-changing and connected world. In: Proceedings of the 7th ACM European Conference on Computer Systems, EuroSys ’12, pp. 85–98. ACM, New York, NY, USA . https://doi.org/10.1145/2168836.2168846

  9. Desikan P, Pathak N, Srivastava J, Kumar V (2005) Incremental page rank computation on evolving graphs. In: Special Interest Tracks and Posters of the 14th International Conference on World Wide Web, WWW ’05, pp. 1094–1095. ACM, New York, NY, USA . https://doi.org/10.1145/1062745.1062885

  10. Doekemeijer N, Varbanescu AL (2014) A survey of parallel graph processing frameworks. In: Delft University of Technology Parallel and Distributed Systems Report Series

  11. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 26(1), 29–41 . https://doi.org/10.1109/3477.484436

  12. Ediger D, McColl R, Riedy J, Bader DA (2012) Stinger: High performance data structure for streaming graphs. In: 2012 IEEE Conference on High Performance Extreme Computing, pp. 1–5 . https://doi.org/10.1109/HPEC.2012.6408680

  13. Fan W, Li J, Luo J, Tan Z, Wang X, Wu Y (2011) Incremental graph pattern matching. In: Proceedings of the 2011 ACM SIGMOD International Conference on Management of Data, SIGMOD ’11, pp. 925–936. ACM, New York, NY, USA . https://doi.org/10.1145/1989323.1989420

  14. Fan W, Liu M, Tian C, Xu R, Zhou J (2020) Incrementalization of graph partitioning algorithms. Proc. VLDB Endow 13(10):1261–1274. https://doi.org/10.14778/3389133.3389142

    Article  Google Scholar 

  15. Fan W, Wang X, Wu Y (2013) Incremental graph pattern matching. ACM Trans. Database Syst. 38(3) https://doi.org/10.1145/2489791

  16. Filippidou I, Kotidis Y (2015) Online and on-demand partitioning of streaming graphs. In: 2015 IEEE International Conference on Big Data (Big Data), pp. 4–13 . https://doi.org/10.1109/BigData.2015.7363735

  17. Gao J, Zhou C, Yu JX (2016) Toward continuous pattern detection over evolving large graph with snapshot isolation. The VLDB Journal 25(2):269–290. https://doi.org/10.1007/s00778-015-0416-z

    Article  Google Scholar 

  18. Glover F, Laguna M (1999) Tabu search I, vol. 1. Springer US . https://doi.org/10.1287/ijoc.1.3.190

  19. Han M, Daudjee K (2015) Giraph unchained: Barrierless asynchronous parallel execution in pregel-like graph processing systems. Proc. VLDB Endow. 8(9), 950–961. https://doi.org/10.14778/2777598.2777604

  20. Han W, Miao Y, Li K, Wu M, Yang F, Zhou L, Prabhakaran V, Chen W, Chen E (2014) Chronos: A graph engine for temporal graph analysis. In: Proceedings of the Ninth European Conference on Computer Systems, EuroSys ’14, pp. 1: 1:14. ACM, New York, NY, USA . https://doi.org/10.1145/2592798.2592799

  21. Hoffman Karla L.and Padberg M, Rinaldi G (2013) Traveling Salesman Problem, pp. 1573–1578. Springer

  22. Holland JH (1975) Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology. Control and Artificial Intelligence. University of Michigan Press, Ann Arbor, MI

    MATH  Google Scholar 

  23. Ji S, Zhao Y, Zhao X (2019) A low-latency computing framework for time-evolving graphs. J. Supercomput. 75(7):3673–3692. https://doi.org/10.1007/s11227-018-2725-7

    Article  Google Scholar 

  24. Kao JS, Chou J (2016) Distributed incremental pattern matching on streaming graphs. In: Proceedings of the ACM Workshop on High Performance Graph Processing, HPGP ’16, pp. 43–50. ACM, New York, NY, USA . https://doi.org/10.1145/2915516.2915519

  25. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp. 1942–1948 vol.4 . https://doi.org/10.1109/ICNN.1995.488968

  26. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680. https://doi.org/10.1126/science.220.4598.671

    Article  MathSciNet  MATH  Google Scholar 

  27. Li B, Gao Z, Niu J, Lv Y, Zhang H (2015) Vertex-centric parallel algorithms for identifying key vertices in large-scale graphs. In: 2015 IEEE 17th International Conference on High Performance Computing and Communications, 2015 IEEE 7th International Symposium on Cyberspace Safety and Security, and 2015 IEEE 12th International Conference on Embedded Software and Systems, pp. 225–231

  28. Lin B, Sun X, Salous S (2016) Solving travelling salesman problem with an improved hybrid genetic algorithm. Journal of Computer and Communications 04:98–106. https://doi.org/10.4236/jcc.2016.415009

    Article  Google Scholar 

  29. Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2):498–516

    Article  MathSciNet  Google Scholar 

  30. Low Y, Gonzalez J, Kyrola A, Bickson D, Guestrin C, Hellerstein J (2010) Graphlab: A new framework for parallel machine learning. In: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, UAI’10, p. 340–349. AUAI Press, Arlington, Virginia, USA

  31. Malewicz G, Austern MH, Bik AJ, Dehnert JC, Horn I, Leiser N, Czajkowski G (2010) Pregel: A system for large-scale graph processing. In: Proceedings of the 2010 ACM SIGMOD International Conference on Management of Data, SIGMOD ’10, pp. 135–146. ACM, New York, NY, USA . https://doi.org/10.1145/1807167.1807184

  32. Noyes D (2018) The top 20 valuable facebook. Web page . https://zephoria.com/top-15-valuable-facebook-statistics/. Last visited on 07/02/2018

  33. Junjie Pan , Dingwei Wang(2006) An ant colony optimization algorithm for multiple travelling salesman problem. In: First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC’06), vol. 1, pp. 210–213

  34. Rapoport A, Horvath WJ (1961) A study of a large sociogram. Behavioral Science 6(4):279–291

    Article  Google Scholar 

  35. Rosenkrantz DJ, Stearns RE, Lewis PM (1974) Approximate algorithms for the traveling salesperson problem. In: Proceedings of the 15th Annual Symposium on Switching and Automata Theory (Swat 1974), SWAT ’74, p. 33–42. IEEE Computer Society, USA . https://doi.org/10.1109/SWAT.1974.4

  36. Roy A, Mihailovic I, Zwaenepoel W (2013) X-stream: Edge-centric graph processing using streaming partitions. In: Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles, SOSP ’13, pp. 472–488. ACM, New York, NY, USA . https://doi.org/10.1145/2517349.2522740

  37. Salihoglu S, Widom J (2013) Gps: A graph processing system. In: Proceedings of the 25th International Conference on Scientific and Statistical Database Management, SSDBM. Association for Computing Machinery, New York, NY, USA . https://doi.org/10.1145/2484838.2484843

  38. Shalini Sharma J (2020) Chou: A survey of computation techniques on time evolving graphs. International Journal of Big Data Intelligence (IJBDI) 01. https://doi.org/10.1504/IJBDI.2020.106151

  39. Simmhan Y, Kumbhare AG, Wickramaarachchi C, Nagarkar S, Ravi S, Raghavendra CS, Prasanna VK (2013) Goffish: A sub-graph centric framework for large-scale graph analytics. CoRR abs/1311.5949 . http://arxiv.org/abs/1311.5949

  40. Tsourakakis C, Gkantsidis C, Radunovic B, Vojnovic M (2014) Fennel: Streaming graph partitioning for massive scale graphs. In: Proceedings of the 7th ACM International Conference on Web Search and Data Mining, WSDM ’14, pp. 333–342. ACM, New York, NY, USA . https://doi.org/10.1145/2556195.2556213

  41. Wang GQ, Wang J, Li M, Li H, Yuan Y (2015) Robot path planning based on the travelling salesman problem. Chemical engineering transactions 46:307–312

    Google Scholar 

  42. Wickramaarachchi C, Frincu M, Prasanna V (2014) Enabling real-time pro-active analytics on streaming graphs. algorithms 15, 18

  43. Yang J, Shi X, Marchese M, Liang Y (2008) Ant colony optimization method for generalized tsp problem. Progress in Natural Science - PROG NAT SCI 18. https://doi.org/10.1016/j.pnsc.2008.03.028

  44. Yuan L, Qin L, Lin X, Chang L, Zhang W (2017) Effective and efficient dynamic graph coloring. Proc. VLDB Endow. 11(3), 338–351 . https://doi.org/10.14778/3157794.3157802

  45. Yuan P, Zhang W, Xie C, Jin H, Liu L, Lee K (2014) Fast iterative graph computation: A path centric approach. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’14, pp. 401–412. IEEE Press, Piscataway, NJ, USA . https://doi.org/10.1109/SC.2014.38

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  1. Institute of Information System and Applications, National Tsing Hua University, Hsinchu, Taiwan

    Shalini Sharma

  2. Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

    Jerry Chou

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Sharma, S., Chou, J. Distributed and incremental travelling salesman algorithm on time-evolving graphs. J Supercomput 77, 10896–10920 (2021). https://doi.org/10.1007/s11227-021-03716-5

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