ABSTRACT
We describe an exact algorithm for traveling salesman problem based on simplified branch-and-bound algorithm developed by E. Balas and N. Christofides, parallelized with OpenMP on a multi-core processor. It has shown better performance than algorithms in preceding articles and works. Our article is intended for people who use parallel programming technologies, deal with mathematical optimization problems, have interest in perspective algorithms for bioinformatics or NP-hard problems.
- 2013. TSPLIB. (2013). Retrieved August 2017 from http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/Google Scholar
- V. V. Burkhovetskiy. 2017. Implementation of the algorithm. (2017). Retrieved August 2017 from http://ops.rsu.ru/works.shtml (in Russian).Google Scholar
- George B. Dantzig. 1998. Linear Programming and Extensions. Princeton University Press, Princeton, NJ, USA, 316--334.Google Scholar
- Egon Balas and Nicos Christofides. 1981. A restricted lagrangean approach to the traveling salesman problem. Mathematical Programming 21, 1 (1981), 19--46. Google ScholarDigital Library
- Michael R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York, NY, USA. Google ScholarDigital Library
- I. I. Melamed, S. I. Sergeyev, and I. H. Sigal. 1989. Zadacha kommivoyazhera. Priblizhennyye algoritmy. Avtomatika i Telemekhanika 54, 11 (1989), 3--26. (in Russian).Google Scholar
- I. I. Melamed, S. I. Sergeyev, and I. H. Sigal. 1989. Zadacha kommivoyazhera. Tochnyye algoritmy. Avtomatika i Telemekhanika 54, 10 (1989), 3--29. (in Russian).Google Scholar
- I. I. Melamed, S. I. Sergeyev, and I. H. Sigal. 1989. Zadacha kommivoyazhera. Voprosy teorii. Avtomatika i Telemekhanika 9 (1989), 3--33. (in Russian).Google Scholar
- Yu. L. Kostuk. 2013. Effektivnaya realizatsiya algoritma resheniya zadachi kommivoyazhera metodom vetvey i granits. Prikladnaya Diskretnaya Matematika 20, 2 (June 2013), 78--90. (in Russian).Google Scholar
- Yu. L. Kostuk. 2013. Modifitsirovanny algoritm resheniya zadachi kommivoyazhera metodom vetvey i granits. Programma i modul s opisaniyem klassa: yazyk Pascal v sisteme Delphi. (2013). Retrieved August 2017 from http://www.inf.tsu.ru/Decanat/Staff.nsf/people/KostjukJuL (in Russian).Google Scholar
- M. Bellmore and G. L. Nemhauser. 1968. The Traveling Salesman Problem: A Survey. Operations Research 16, 3 (1968), 538--558.Google ScholarDigital Library
- M. A. Posypkin and I. H. Sigal. 2008. Kombinirovanny Parallelny Algoritm Resheniya Zadachi o Rantse. In Parallelnyye Vychisleniya i Zadachi Upravleniya (PACO'2008). 177--189. (in Russian).Google Scholar
- D. V. Makoshenko. 2011. Analiticheskoye Predskazaniye Vremeni Ispolneniya Programm i Osnovannyye na nem Metody Optimizatsii. Ph.D. Dissertation. Southern Federal University, Russia. (in Russian).Google Scholar
- Sara El-Metwally, Osama M. Ouda, and Mohamed Helmy. 2014. Next Generation Sequencing Technologies and Challenges in Sequence Assembly. Springer, 17--19, 84--85.Google Scholar
- Paolo Toth. 2008. Exact algorithms for the asymmetric traveling salesman problem. (2008). Retrieved August 2017 from http://www.graphalgorithms.it/erice2008/Talks/ATSP_Lecture_Erice_Toth.pdfGoogle Scholar
- Virat Agarwal, Fabrizio Petrini, Davide Pasetto, and David A. Bader. 2010. Scalable Graph Exploration on Multicore Processors. In Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE Computer Society Washington, DC, USA, 1--11. Google ScholarDigital Library
- V. V. Burkhovetskiy and B. Ya. Steinberg. 2016. Issledovaniye Vozmozhnosti Rasparallelivaniya Algoritma Littla s Modifikatsiyey Kostuka dla Resheniya Zadachi Kommivoyazhera. In National Supercomputing Forum 2016 (NSCF'2016). Retrieved August 2017 from http://2016.nscf.ru/TesisAll/04_Reshenie_zadach_optimizatsii/736_BurkhovetskiyVV.pdf (in Russian).Google Scholar
- V. V. Burkhovetskiy and B. Ya. Steinberg. 2017. Strategiya Ispolzovaniya Krupnikh Zadaniy pri Parallelnom Obkhode Dereva. In Yazyki Programmirovaniya i Kompilatory 2017 (PLC'2017). 66--70. Retrieved August 2017 from http://plc.sfedu.ru/files/PLC-2017-proceedings.pdf (in Russian).Google Scholar
- Y. G. Evtushenko, I.V. Golubeva, Y. V. Orlov, and M. A. Posypkin. 2016. Using simulation for performance analysis and visualization of parallel Branch-and-Bound methods. In Russian Supercomputing Days 2016. Retrieved August 2017 from http://russianscdays.org/files/pdf16/41.pdfGoogle Scholar
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- An exact parallel algorithm for traveling salesman problem
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