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Bellman–Ford algorithm
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== References == === Original sources === *{{cite conference | last = Shimbel | first = A. | title = Structure in communication nets | location = New York, New York | pages = 199–203 | publisher = Polytechnic Press of the Polytechnic Institute of Brooklyn | conference = Proceedings of the Symposium on Information Networks | year = 1955}} *{{cite journal | last = Bellman | first = Richard | author-link = Richard Bellman | mr = 0102435 | journal = Quarterly of Applied Mathematics | pages = 87–90 | title = On a routing problem | volume = 16 | year = 1958 | doi = 10.1090/qam/102435 | doi-access = free }} *{{cite book |author-link=L. R. Ford Jr. | last=Ford | first=Lester R. Jr. |title=Network Flow Theory |date=August 14, 1956 |series=Paper P-923 |publisher=RAND Corporation |location=Santa Monica, California |url=http://www.rand.org/pubs/papers/P923.html}} *{{cite conference | last = Moore | first = Edward F. | author-link = Edward F. Moore | title = The shortest path through a maze | location = Cambridge, Massachusetts | mr = 0114710 | pages = 285–292 | publisher = Harvard Univ. Press | conference = Proc. Internat. Sympos. Switching Theory 1957, Part II | year = 1959}} *{{cite journal | last = Yen | first = Jin Y. | mr = 0253822 | journal = Quarterly of Applied Mathematics | pages = 526–530 | title = An algorithm for finding shortest routes from all source nodes to a given destination in general networks | volume = 27 | year = 1970 | issue = 4 | doi = 10.1090/qam/253822 | doi-access = free }} *{{cite conference|contribution=Randomized speedup of the Bellman–Ford algorithm|first1=M. J.|last1=Bannister|first2=D.|last2=Eppstein|author2-link=David Eppstein|arxiv=1111.5414|title=Analytic Algorithmics and Combinatorics (ANALCO12), Kyoto, Japan|year=2012|pages=41–47|doi=10.1137/1.9781611973020.6}} *{{cite conference | last = Fineman | first = Jeremy T. | editor1-last = Mohar | editor1-first = Bojan | editor2-last = Shinkar | editor2-first = Igor | editor3-last = O'Donnell | editor3-first = Ryan | arxiv = 2311.02520 | contribution = Single-source shortest paths with negative real weights in <math>\tilde O(mn^{8/9})</math> time | doi = 10.1145/3618260.3649614 | pages = 3–14 | publisher = Association for Computing Machinery | title = Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, Vancouver, BC, Canada, June 24–28, 2024 | year = 2024}} === Secondary sources === *{{cite book | last1 = Ford | first1 = L. R. Jr. | author1-link = L. R. Ford Jr. | last2 = Fulkerson | first2 = D. R. | author2-link = D. R. Fulkerson | contribution = A shortest chain algorithm | pages = 130–134 | publisher = Princeton University Press | title = Flows in Networks | year = 1962}} *{{Cite book|first1=Jørgen |last1=Bang-Jensen|first2=Gregory|last2=Gutin|year=2000|title=Digraphs: Theory, Algorithms and Applications|edition=First |isbn=978-1-84800-997-4|chapter=Section 2.3.4: The Bellman-Ford-Moore algorithm|publisher=Springer |url=http://www.cs.rhul.ac.uk/books/dbook/}} *{{cite journal|first=Alexander|last=Schrijver|title=On the history of combinatorial optimization (till 1960)|pages=1–68|publisher=Elsevier|journal=Handbook of Discrete Optimization|year=2005|url=http://homepages.cwi.nl/~lex/files/histco.pdf}} *{{Introduction to Algorithms}}, Fourth Edition. MIT Press, 2022. {{ISBN|978-0-262-04630-5}}. Section 22.1: The Bellman–Ford algorithm, pp. 612–616. Problem 22–1, p. 640. *{{cite book | first1 = George T. | last1 = Heineman | first2 = Gary | last2 = Pollice | first3 = Stanley | last3 = Selkow | title= Algorithms in a Nutshell | publisher=[[O'Reilly Media]] | year=2008 | chapter=Chapter 6: Graph Algorithms | pages = 160–164 | isbn=978-0-596-51624-6 }} *{{cite book|last1=Kleinberg|first1=Jon|author1-link=Jon Kleinberg|last2=Tardos|first2=Éva|author2-link=Éva Tardos|year=2006|title=Algorithm Design|location=New York|publisher=Pearson Education, Inc.}} *{{Cite book|first=Robert|last=Sedgewick|author-link=Robert Sedgewick (computer scientist)|year=2002|title=Algorithms in Java|edition=3rd|isbn=0-201-36121-3|chapter=Section 21.7: Negative Edge Weights|publisher=Addison-Wesley |url=http://safari.oreilly.com/0201361213/ch21lev1sec7|access-date=2007-05-28|archive-url=https://web.archive.org/web/20080531142256/http://safari.oreilly.com/0201361213/ch21lev1sec7|archive-date=2008-05-31|url-status=dead}} {{Graph traversal algorithms}} {{DEFAULTSORT:Bellman-Ford algorithm}} [[Category:Graph algorithms]] [[Category:Polynomial-time problems]] [[Category:Articles with example C code]] [[Category:Articles with example pseudocode]] [[Category:Dynamic programming]] [[Category:Graph distance]]
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