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The Complexity of Combinatorial Computations: An Introduction

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Book cover GI — 8. Jahrestagung

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 16))

Abstract

The search for mechanizable procedures or algorithms for solving problems has been an integral part of mathematics from the beginning. Concern about the efficiency of the algorithms discovered was rarely mentioned explicitly, however, until the last few decades. Nevertheless, we must presume that this concern was often present, since such algorithms as Gaussian elimination for solving linear equations, Newton’s iteration for algebraic equations, and Euclid’s algorithm for greatest common divisors, appear very efficient even now after centuries of further investigation.

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References

  1. A. Aho, J. Hopcroft and J. Ullman. The Design and Analysis of Computer Algorithms. Addison Wesley (1974).

    MATH  Google Scholar 

  2. D. Angluin and L. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. Proc. 9th ACM Symp. on Theory of Computing. (1977).

    Google Scholar 

  3. M. Blum. A machine-independent theory of the complexity of recursive functions. JACM 14 (1967) 322.

    Article  MATH  Google Scholar 

  4. S. Cook. The complexity of theorem proving procedures. Proc. 3rd ACM Symp. on Theory of Computing (1971) 151.

    Google Scholar 

  5. J. Edmonds. Paths, trees and flowers. Can. J. Math 17 (1965) 499.

    Article  MathSciNet  Google Scholar 

  6. P. Erdos and A. Renyi. On random graphs I, Publ. Math. 6 (1959) 290.

    MathSciNet  Google Scholar 

  7. S. Even and O. Kariv. An 0(n2.5) algorithm for maximum matching in general

    Google Scholar 

  8. graphs. Proc. 16th IEEE Symp. on FOCS (1975) 100.

    Google Scholar 

  9. L. Ford and D. Fulkerson. Flows in Networks. Princeton Univ. Press, (1962).

    MATH  Google Scholar 

  10. M. Garey and D. Johnson. Performance guarantees for heuristic algorithms. In “Algorithms and Complexity”, J.F. Traub (ed), Academic Press (1976).

    Google Scholar 

  11. G. Grimmett and C. McDiarmid. On colouring random graphs. Math. Proc. Camb. Phil. Soc. 77 (1975) 313.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Hopcroft and R. Karp. An n2.5 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2 (1973) 225.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Hopcroft and R. Tarjan. Efficient planarity testing. JACM 21 (1974) 549.

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Johnson et al. Performance bounds for simple one dimensional bin-packing algorithms. SIAM J. Comput. 3 (1974) 299.

    Article  MathSciNet  Google Scholar 

  15. R. Karp. Reducibility among combinatorial problems. In Complexity of Computer Computations, R.E. Miller and J.W. Thatcher (eds). Plenum Press, N.Y. (1972) 85.

    Google Scholar 

  16. R. Karp. Probabilistic analysis of partitioning algorithms for the travelling salesman problem in the plane. Math. of Operations Research, Aug. 1977.

    Google Scholar 

  17. R. Karp. A patching algorithm for the nonsymmetric travelling salesman problem. SIAM J. on Comput. (to appear).

    Google Scholar 

  18. P. Kasteleyn. Graph theory and crystal physics. In Graph Theory and Theoretical Physics, F. Harary (ed), Academic Press (1967) 43.

    Google Scholar 

  19. G. Kirchhoff. Ann. Phys. Chem, 72, (1847) 497.

    Article  Google Scholar 

  20. V. Klee and G. Minty. How good is the simplex alaorithm? Proc. 3rd Symp. on Inequalities, UCLA. O. Shisha (Ed), Academic Press, (1969) 159.

    Google Scholar 

  21. D. Khuth. Mathematics and computer science: coping with finiteness. Science 194 (1976) 1235.

    Article  MathSciNet  Google Scholar 

  22. D. Knuth and A. Schonhage. The expected linearity of a simple equivalence algorithm. Theoretical Comp. Sci. 6 (1978) 281.

    Article  MathSciNet  MATH  Google Scholar 

  23. A. Korsunov. Solution of a problem of Erdos and Renyi on Hamiltonian cycles in nonoriented graphs. Soviet Math. Dokl. 17 (1976) 760.

    MATH  Google Scholar 

  24. L. Levin. Universal combinatorial problems. Probl. Peredaci Informacii 9 (1972) 115.

    Google Scholar 

  25. A. Meyer and L. Stockmeyer. The equivalence problem for regular expressions with squarring requires exponential space. Proc. 13th IEEE Symp. on SWAT

    Google Scholar 

  26. (1972) 125.

    Google Scholar 

  27. G. Miller. Riemann’s hypothesis and tests for primality. Proc. 7th ACM Symp. on Theory of Computing (1975) 234.

    Google Scholar 

  28. L. Posa. Hamiltonian circuits in random graphs. Discrete Mathematics. 14 (1976) 359.

    Article  MathSciNet  MATH  Google Scholar 

  29. M. Rabin. Complexity of Computations CACM 20 (1977) 625.

    MathSciNet  MATH  Google Scholar 

  30. M. Rabin. Probabilistic algorithms. In Algorithms and Complexity, J.F. Traub. (ed) Academic Press (1976) 21.

    Google Scholar 

  31. R. Rivest, A. Shamir and L. Adleman. A method for obtaining digital signatures and public-key cryptosystems. CACM 21. (1978) 120.

    MathSciNet  MATH  Google Scholar 

  32. C. Schnorr. Optimal algorithms for self-reducible problems. Proc. 3rd Coll. on Automata, Languages and Programming, S. Michaelson and R. Milner (eds) Edinburgh U. Press (1976) 322.

    Google Scholar 

  33. R. Solovay and V. Strassen. A fast Monte-Carlo test for primality. SIAM J. Comput. 6 (1977) 84.

    Article  MathSciNet  MATH  Google Scholar 

  34. R. Tarjan. Depth first search and linear graph algorithms. SIAM J. Computing 1 (1972) 146.

    Article  MathSciNet  MATH  Google Scholar 

  35. R. Tarjan. Complexity of Combinatorial algorithms. Tech. Rep. STAN-CS-77–601, CS. Dept, Stanford University (1977).

    Google Scholar 

  36. L. Valiant. Conplexity of enumeration and reliability problems. SIAM J. on Comput. (to appear).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Edinburgh University, Edinburgh, Scotland

    L. G. Valiant

Authors
  1. L. G. Valiant
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Editor information

Editors and Affiliations

  1. Institut für Softwaretechnik und theoretische Informatik Fachbereich Informatik (20) Fachgebiet Betriebssysteme, TU Berlin, Ernst-Reuter-Platz 7, 1000, Berlin 10, Deutschland

    Sigram Schindler

  2. Institut für technische Informatik, TU Berlin, Einsteinufer 35/37, 1000, Berlin 10, Deutschland

    Wolfgang K. Giloi

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© 1978 Springer-Verlag Berlin · Heidelberg

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Valiant, L.G. (1978). The Complexity of Combinatorial Computations: An Introduction. In: Schindler, S., Giloi, W.K. (eds) GI — 8. Jahrestagung. Informatik-Fachberichte, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-67091-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-67091-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09038-0

  • Online ISBN: 978-3-642-67091-6

  • eBook Packages: Springer Book Archive

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