The Christofides algorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric space (they are symmetric and obey the triangle inequality).[1]
It is an approximation algorithm that guarantees that its solutions will be within a factor of 3/2 of the optimal solution length, and is named after Nicos Christofides and Anatoliy I. Serdyukov (Russian: Анатолий Иванович Сердюков); the latter discovered it independently in 1976 (but the publication is dated 1978).[2][3][4]
^Goodrich, Michael T.; Tamassia, Roberto (2015), "18.1.2 The Christofides Approximation Algorithm", Algorithm Design and Applications, Wiley, pp. 513–514.
^Christofides, Nicos (1976), Worst-case analysis of a new heuristic for the travelling salesman problem(PDF), Report 388, Graduate School of Industrial Administration, CMU, archived (PDF) from the original on July 21, 2019
^van Bevern, René; Slugina, Viktoriia A. (2020), "A historical note on the 3/2-approximation algorithm for the metric traveling salesman problem", Historia Mathematica, 53: 118–127, arXiv:2004.02437, doi:10.1016/j.hm.2020.04.003, S2CID 214803097
^Serdyukov, Anatoliy (1978), "О некоторых экстремальных обходах в графах" [On some extremal walks in graphs] (PDF), Upravlyaemye Sistemy (Управляемые системы) (in Russian), 17: 76–79
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The Christofidesalgorithm or Christofides–Serdyukov algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on...
he devised Christofidesalgorithm, an algorithm for finding approximate solutions to the travelling salesman problem. Christofidesalgorithm is considered...
space was the very simple Christofidesalgorithm which produced a path at most 50% longer than the optimum. (Many other algorithms could usually do much better...
given binary relation Traveling salesman problem Christofidesalgorithm Nearest neighbour algorithm Warnsdorff's rule: a heuristic method for solving...
above). They are invoked as subroutines in algorithms for other problems, including the Christofidesalgorithm for approximating the traveling salesman...
In 1976, Christofides and Serdyukov (independently of each other) made a big advance in this direction: the Christofides-Serdyukov algorithm yields a...
Schmied. Coupled with the knowledge of the existence of Christofides' 1.5 approximation algorithm, this tells us that the threshold of approximability for...
constraints, they were first proposed for the TSP and subsequently extended by Christofides, Mingozzi and Toth. u j − u i ≥ d j − C ( 1 − x i j ) ∀ i...
Springer-Verlag, pp. 32–34, ISBN 978-1-84800-997-4. Christofides, Nicos (1975), Graph theory: an algorithmic approach, Academic Press, pp. 170–174. Mitrani...
and at least as hard to approximate. An approximation algorithm based on the Christofidesalgorithm for the traveling salesperson problem can approximate...
Christofides, Nicos (1975), Graph theory: an algorithmic approach, Academic Press, pp. 170–174 Di Battista, G.; Tamassia, R. (1988), "Algorithms for...
later shown that both algorithms contained errors. Beasley presented a correct dynamic programming algorithm. Herz and Christofides and Whitlock presented...
www.digitaltrends.com. March 26, 2018. Retrieved February 6, 2019. Christofides, E.; Muise, A.; Desmarais, S. (March 31, 2010). "Privacy and Disclosure...
seven bridges in Königsberg without repeating a bridge. In the Christofides–Serdyukov algorithm for approximating the traveling salesperson problem, the geometric...
journal}}: CS1 maint: multiple names: authors list (link) Muise, A., Christofides, E., & Demsmarais, S. (2014). " Creeping" or just information seeking...
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