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Travelling salesman problem
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==References== {{Refbegin|40em}} *{{Citation | last1 = Applegate | first1 = D. L. | last2 = Bixby | first2 = R. M. | last3 = ChvΓ‘tal | first3 = V. | last4 = Cook|author4-link=William J. Cook | year = 2006 | title = The Traveling Salesman Problem|first4 =W. J. | publisher = Princeton University Press | isbn = 978-0-691-12993-8}}. *{{Citation | last1 = Allender | first1 = Eric | last2 = BΓΌrgisser | first2 = Peter | last3 = Kjeldgaard-Pedersen | first3 = Johan | last4 = Mitersen | first4 = Peter Bro | year = 2007 | title = On the Complexity of Numerical Analysis | url = https://www3.math.tu-berlin.de/algebra/work/focs7.pdf | journal = [[SIAM J. Comput.]] | volume=38 | issue=5 | pages = 1987β2006 | doi=10.1137/070697926 | citeseerx = 10.1.1.167.5495 }}. *{{Citation | last = Arora | first = Sanjeev | author-link = Sanjeev Arora | doi = 10.1145/290179.290180 | issue = 5 | journal = [[Journal of the ACM]] | mr = 1668147 | pages = 753β782 | title = Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems | volume = 45 | year = 1998 | s2cid = 3023351 |url=http://graphics.stanford.edu/courses/cs468-06-winter/Papers/arora-tsp.pdf}}. *{{Citation |last1= Beardwood |first1=J. |last2=Halton |first2=J.H. |last3=Hammersley |first3=J.M. |title=The Shortest Path Through Many Points |journal= Proceedings of the Cambridge Philosophical Society |volume =55 |issue=4 |pages= 299β327 |date=October 1959 |doi=10.1017/s0305004100034095|bibcode=1959PCPS...55..299B |s2cid=122062088 |issn=0305-0041 |url=https://www.cambridge.org/core/product/identifier/S0305004100034095/type/journal_article }}. *{{Citation |last= Bellman |first= R. |contribution= Combinatorial Processes and Dynamic Programming |title= Combinatorial Analysis, Proceedings of Symposia in Applied Mathematics 10 |editor1= Bellman, R. |editor2=Hall, M. Jr. |pages= 217β249 |publisher= American Mathematical Society |year=1960 }}. *{{Citation |last= Bellman |first= R. |title= Dynamic Programming Treatment of the Travelling Salesman Problem |journal= Journal of the Association for Computing Machinery |volume=9|pages= 61β63 |year=1962|doi=10.1145/321105.321111|s2cid= 15649582 |doi-access= free}}. *{{citation | last1 = Berman | first1 = Piotr | last2 = Karpinski | first2 = Marek | author2-link = Marek Karpinski | contribution = 8/7-approximation algorithm for (1,2)-TSP | doi = 10.1145/1109557.1109627 | id = {{ECCC|2005|05|069}} | pages = 641β648 | title = Proc. 17th ACM-SIAM Symposium on Discrete Algorithms (SODA '06) | year = 2006 | isbn = 978-0-89871-605-4| url = http://eccc.hpi-web.de/report/2005/069/revision/2/download/| citeseerx = 10.1.1.430.2224 | s2cid = 9054176 }}. *{{Citation |last=Christofides|first=N.|year= 1976 |title=Worst-case analysis of a new heuristic for the travelling salesman problem |series=Technical Report 388|publisher=Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh}}. *{{Citation|last1=Hassin|first1= R.|last2= Rubinstein|first2= S.|year=2000 |title=Better approximations for max TSP |journal=Information Processing Letters|volume=75|pages=181β186|doi=10.1016/S0020-0190(00)00097-1|issue=4|citeseerx= 10.1.1.35.7209}}. *{{Citation | last1 = Held | first1 = M. | author1-link = Michael Held | last2 = Karp | first2 = R. M. | author2-link = Richard Karp | year = 1962 | title = A Dynamic Programming Approach to Sequencing Problems | journal = Journal of the Society for Industrial and Applied Mathematics | volume = 10 | issue = 1 | pages = 196β210 | doi = 10.1137/0110015 }}. *{{Citation |last1= Kaplan|first1=H.|last2=Lewenstein |first2=L. | last3=Shafrir|first3=N. |last4= Sviridenko|first4=M.|contribution= Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs |title= Proc. 44th IEEE Symp. on Foundations of Comput. Sci |pages= 56β65|year= 2004}}. *{{Citation |last1=Karpinski|first1=M. |last2=Lampis|first2=M. |last3=Schmied|first3=R. |journal=Journal of Computer and System Sciences |volume=81 |issue=8 |year=2015 |title=New Inapproximability bounds for TSP |pages=1665β1677 |doi=10.1016/j.jcss.2015.06.003 |arxiv=1303.6437 }} *{{Citation |last1= Kosaraju|first1= S. R.|last2= Park|first2=J. K. |last3= Stein|first3= C. |year=1994 |contribution=Long tours and short superstrings' |title=Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci |publisher= IEEE Computer Society|pages= 166β177}}. *{{Citation | last1 = Larson | first1 = Richard C. | last2 = Odoni | first2 = Amedeo R. | year = 1981 | title = Urban Operations Research | chapter-url = http://web.mit.edu/urban_or_book/www/book/chapter6/6.4.7.html | chapter=6.4.7: Applications of Network Models Β§ Routing Problems Β§Β§ Euclidean TSP | publisher = Prentice-Hall | isbn = 978-0-13-939447-8 | oclc = 6331426 }}. *{{Citation |last1=Padberg|first1=M.|last2=Rinaldi|first2=G. |title=A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems |journal = SIAM Review |volume=33|year = 1991 |pages = 60β100 |doi = 10.1137/1033004|s2cid=18516138}}. *{{citation | last = Papadimitriou | first = Christos H. | author-link = Christos Papadimitriou | issue = 3 | journal = Theoretical Computer Science | mr = 0455550 | pages = 237β244 | title = The Euclidean traveling salesman problem is NP-complete | volume = 4 | year = 1977 | doi = 10.1016/0304-3975(77)90012-3| doi-access = free }}. *{{Citation | last1=Papadimitriou | first1=Christos H. | last2=Yannakakis | first2=Mihalis | authorlink2=Mihalis Yannakakis | date=1993 | title=The traveling salesman problem with distances one and two | journal=[[Mathematics of Operations Research]] | volume=18 | pages=1β11 | doi=10.1287/moor.18.1.1}}. * {{cite book |chapter=On the history of combinatorial optimization (till 1960) |editor1=[[Karen Aardal|K. Aardal]] |editor2=[[George Nemhauser|G.L. Nemhauser]] |editor3=R. Weismantel |title=Handbook of Discrete Optimization |year=2005 |first=Alexander |last=Schrijver |author-link=Alexander Schrijver |publisher=Elsevier |place=Amsterdam |pages=1β68 |url=http://homepages.cwi.nl/~lex/files/histco.pdf}} *{{Citation |last=Serdyukov|first= A. I.|year= 1984 |title=An algorithm with an estimate for the traveling salesman problem of the maximum' |journal=Upravlyaemye Sistemy |volume= 25|pages= 80β86}}. *{{citation | last = Steinerberger | first = Stefan | journal = Advances in Applied Probability | title = New Bounds for the Traveling Salesman Constant | year = 2015 | volume = 47 |issue=1 | pages = 27β36 | doi = 10.1239/aap/1427814579 | arxiv = 1311.6338| s2cid = 119293287 |bibcode=2013arXiv1311.6338S }}. *{{Citation | author-link = Gerhard J. Woeginger |last= Woeginger|first= G.J.|contribution= Exact Algorithms for NP-Hard Problems: A Survey |title=Combinatorial Optimization β Eureka, You Shrink! Lecture notes in computer science, vol. 2570 |pages= 185β207|publisher= Springer |year=2003 }}. {{Refend}}
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