• computer science, the HopcroftKarp algorithm (sometimes more accurately called the HopcroftKarp–Karzanov algorithm) is an algorithm that takes a bipartite...
    25 KB (3,746 words) - 14:52, 14 May 2025
  • Thumbnail for Richard M. Karp
    21 problems to be NP-complete. In 1973 he and John Hopcroft published the HopcroftKarp algorithm, the fastest known method for finding maximum cardinality...
    12 KB (883 words) - 20:13, 31 May 2025
  • Thumbnail for John Hopcroft
    analysis of algorithms and data structures." Along with his work with Tarjan on planar graphs he is also known for the HopcroftKarp algorithm for finding...
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  • Thumbnail for Maximum cardinality matching
    this algorithm is given by the more elaborate HopcroftKarp algorithm, which searches for multiple augmenting paths simultaneously. This algorithm runs...
    10 KB (1,317 words) - 15:41, 14 June 2025
  • {\displaystyle O({\sqrt {V}}E)} time bound. The resulting algorithm is also known as HopcroftKarp algorithm. More generally, this bound holds for any unit network...
    12 KB (1,693 words) - 17:06, 20 November 2024
  • Coloring algorithm: Graph coloring algorithm. HopcroftKarp algorithm: convert a bipartite graph to a maximum cardinality matching Hungarian algorithm: algorithm...
    72 KB (7,951 words) - 17:13, 5 June 2025
  • march algorithm developed by R. A. Jarvis 1973 – HopcroftKarp algorithm developed by John Hopcroft and Richard Karp 1974 – Pollard's p − 1 algorithm developed...
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  • Thumbnail for Bipartite graph
    graphs than on non-bipartite graphs, and many matching algorithms such as the HopcroftKarp algorithm for maximum cardinality matching work correctly only...
    33 KB (4,086 words) - 21:34, 28 May 2025
  • Thumbnail for 3-dimensional matching
    2-dimensional matching), for example, the HopcroftKarp algorithm. There is a very simple polynomial-time 3-approximation algorithm for 3-dimensional matching: find...
    13 KB (1,550 words) - 00:09, 5 December 2024
  • Thumbnail for Kőnig's theorem (graph theory)
    described above provides an algorithm for producing a minimum vertex cover given a maximum matching. Thus, the HopcroftKarp algorithm for finding maximum matchings...
    24 KB (3,433 words) - 02:46, 12 December 2024
  • by the Hopcroft-Karp algorithm in time O(√VE) time, and there are more efficient randomized algorithms, approximation algorithms, and algorithms for special...
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  • Thumbnail for Vector addition system
    introduced by Richard M. Karp and Raymond E. Miller in 1969, and generalized to vector addition systems with states (VASS) by John E. Hopcroft and Jean-Jacques...
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  • Ullman (1974), Theorem 10.4. Aho, Hopcroft & Ullman (1974), Theorem 10.5. Schöning, Uwe (Oct 1999). "A probabilistic algorithm for k-SAT and constraint satisfaction...
    45 KB (4,870 words) - 16:46, 24 June 2025
  • Thumbnail for NP-completeness
    popularized by Alfred Aho, John Hopcroft and Jeffrey Ullman in their celebrated textbook "The Design and Analysis of Computer Algorithms". He reports that they...
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  • such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory...
    50 KB (6,704 words) - 04:30, 7 July 2025
  • Thumbnail for Rajeev Motwani
    textbooks: Randomized Algorithms with Prabhakar Raghavan and Introduction to Automata Theory, Languages, and Computation with John Hopcroft and Jeffrey Ullman...
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  • Hopcroft & Ullman 1979, pp. 19–20. Alfred V. Aho and John E. Hopcroft and Jeffrey D. Ullman (1974). The Design and Analysis of Computer Algorithms. Reading/MA:...
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  • Syntactic pattern recognition (category Classification algorithms)
    recognition. A graph matching algorithm will yield the optimal correspondence. Grammar induction String matching HopcroftKarp algorithm Structural information...
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  • inventor of preflow-push based algorithms for the maximum flow problem, and the co-inventor of the HopcroftKarp–Karzanov algorithm for maximum matching in bipartite...
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  • a bipartite graph, which is solvable in polynomial time by the HopcroftKarp algorithm. For a bipartite graph with 2n vertices partitioned into two parts...
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  • Donald Knuth, Robert Floyd, Stephen Cook, Niklaus Wirth, Richard Karp, John Hopcroft, Robert Tarjan, Ronald Rivest, Edmund Clarke, Judea Perl, Silvio...
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  • Thumbnail for Network controllability
    by working in the bipartite representation using the classical HopcroftKarp algorithm, which runs in O(E√N) time in the worst case. For undirected graph...
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  • x0. The algorithm for finding a Hall violator proceeds as follows. Find a maximum matching M (it can be found with the HopcroftKarp algorithm). If all...
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  • (context-free grammars) Hopcroft and Ullman 1979 (p.229, exercise 9.2) call it a normal form for right-linear grammars. Hopcroft and Ullman 1979, p.218-219...
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  • ISBN 978-3-540-32880-3. Aho, Alfred V.; Hopcroft, John E.; Ullman, Jeffrey D. (1974). The Design and Analysis of Computer Algorithms. Addison-Wesley. ISBN 978-0-201-00029-0...
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    pp. 3–6 Serebryakov et al. (2006), pp. 50–54 Рубцов (2019), pp. 89–94 Hopcroft & Ullman (1979), pp. 65–68 Blumer et al. (1984), pp. 111–114 Crochemore...
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  • Jails, Varnish cache David Karger Richard Karp – NP-completeness Narendra Karmarkar – Karmarkar's algorithm Marek Karpinski – NP optimization problems...
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  • Thumbnail for Turing Award
    Archived from the original on July 4, 2017. Retrieved March 4, 2024. "John E. Hopcroft - A.M. Turing Award Laureate". Association for Computing Machinery. Archived...
    80 KB (3,581 words) - 00:11, 20 June 2025
  • ISBN 978-0-19-162080-5. A. P. Ershov, Donald Ervin Knuth, ed. (1981). Algorithms in modern mathematics and computer science: proceedings, Urgench, Uzbek...
    68 KB (1,578 words) - 14:53, 12 July 2025