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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

New results on the average behavior of simplex algorithms
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by Ilan Adler, Nimrod Megiddo and Michael J. Todd PDF
Bull. Amer. Math. Soc. 11 (1984), 378-382
References
    [A] I. Adler, The expected number of pivots needed to solve parametric linear programs and the efficiency of the self-dual simplex method, Dept. Industrial Engineering and Operations Res., Univ. of California, Berkeley, June 1983. [AKS] I. Adler, R. M. Karp and R. Shamir, A simplex variant solving an m × d linear program in O (min (m2, d2)) expected number of steps, Report UCB CSD 83/158, Computer Science Division, Univ. of California, Berkeley, December 1983. [AM1] I. Adler and N. Megiddo, A simplex-type algorithm solves linear programming problems of order m × n in only O ((min (m, n))2) steps on the average, November 1983 (manuscript).
  • Ilan Adler and Nimrod Megiddo, A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension, J. Assoc. Comput. Mach. 32 (1985), no. 4, 871–895. MR 810342, DOI 10.1145/4221.4222
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  • Karl-Heinz Borgwardt, Some distribution-independent results about the asymptotic order of the average number of pivot steps of the simplex method, Math. Oper. Res. 7 (1982), no. 3, 441–462. MR 667934, DOI 10.1287/moor.7.3.441
  • K.-H. Borgwardt, The average number of pivot steps required by the simplex-method is polynomial, Z. Oper. Res. Ser. A-B 26 (1982), no. 5, A157–A177 (English, with German summary). MR 686603, DOI 10.1007/bf01917108
  • George B. Dantzig, Linear programming and extensions, Princeton University Press, Princeton, N.J., 1963. MR 0201189
  • [H] M. Haimovich, The simplex algorithm is very good!–On the expected number of pivot steps and related properties of random linear programs, Columbia Univ., New York, April 1983 (manuscript).
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  • [K] L. G. Khachian, A polynomial algorithm in linear programming, Soviet Math. Dokl. 20 (1979), 191-194. [Me1] N. Megiddo, Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm, Dept. of Computer Science, Stanford Univ., September 1983 (preliminary report). [Me2] N. Megiddo, A note on the generality of the self-dual algorithm with various starting points, Dept. of Computer Science, Stanford Univ., December 1983 (preliminary report).
  • Katta G. Murty, Computational complexity of parametric linear programming, Math. Programming 19 (1980), no. 2, 213–219. MR 583280, DOI 10.1007/BF01581642
  • Steve Smale, On the average number of steps of the simplex method of linear programming, Math. Programming 27 (1983), no. 3, 241–262. MR 725621, DOI 10.1007/BF02591902
  • S. Smale, The problem of the average speed of the simplex method, Mathematical programming: the state of the art (Bonn, 1982) Springer, Berlin, 1983, pp. 530–539. MR 717413
  • [T] M. J. Todd, Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programrning problems, Tech. Rep. No. 595, School of Operations Res. and Industrial Enginnering, Cornell Univ., 1983.
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 11 (1984), 378-382
  • MSC (1980): Primary 68C25; Secondary 90C05
  • DOI: https://doi.org/10.1090/S0273-0979-1984-15317-5
  • MathSciNet review: 752803