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Book Review

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Book Information:

Author: Kazuo Murota
Title: Discrete convex analysis
Additional book information: SIAM Monographs on Discrete Mathematics and Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003, xxii+389 pp., ISBN 0-89871-540-7, $111.00

References [Enhancements On Off] (What's this?)

  • [BM03] I. Bárány and J. Matousek, A fractional Helly theorem for convex lattice sets, Adv. Math. 174 (2003), 227-235. MR 2003m:52006
  • [Br88] M. Brion, Points entiers dans les polyèdres convexes (French), Ann. Sci. École Norm. Sup. (4) 21 (1988), 653-663. MR 90d:52020
  • [C97] J.W.S. Cassels, An Introduction to the Geometry of Numbers, Corrected reprint of the 1971 edition. Classics in Mathematics, Springer-Verlag, Berlin, 1997. MR 97i:11074
  • [DK03] V.I. Danilov and A. Koshevoy, Discrete convexity and unimodularity. I, preprint arXiv:math.CO/0304291, 2003.
  • [Do73] J.-P. Doignon, Convexity in cristallographical lattices, J. Geometry 3 (1973), 71-85. MR 52:7937
  • [G74] M.B. Gromova, The Birkhoff-von Neumann theorem for polystochastic matrices (Russian), Operations Research and Statistical Simulation, No. 2, Izdat. Leningrad. Univ., Leningrad, 1974, pp. 3-15; Selected translations. Selecta Math. Soviet. 11 (1992), no. 2, 145-158. MR 92m:00062, MR 52:448
  • [GLS93] M. Grötschel, L. Lovász, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization (Second edition), Algorithms and Combinatorics, 2, Springer-Verlag, Berlin, 1993. MR 95e:90001
  • [L91] J. Lawrence, Rational-function-valued valuations on polyhedra, Discrete and computational geometry (New Brunswick, NJ, 1989/1990), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 6, Amer. Math. Soc., Providence, RI, 1991, pp. 199-208. MR 92m:52025
  • [M02] J. Matousek, Lectures on Discrete Geometry, Graduate Texts in Mathematics, 212, Springer-Verlag, New York, 2002. MR 2003f:52011
  • [P78] C.H. Papadimitriou, The adjacency relation on the traveling salesman polytope is NP-complete, Math. Programming 14 (1978), 312-324. MR 58:20422
  • [PK92] A.V. Pukhlikov and A.G. Khovanskii, The Riemann-Roch theorem for integrals and sums of quasipolynomials on virtual polytopes (Russian), Algebra i Analiz 4 (1992), 188-216; translation in St. Petersburg Math. J. 4 (1993), no. 4, 789-812. MR 94c:14044
  • [S97] H.E. Scarf, Test sets for integer programs. Lectures on mathematical programming (ismp97) (Lausanne, 1997), Math. Programming, Ser. B 79 (1997), 355-368. MR 98e:90098
  • [Sc03] A. Schrijver, Combinatorial Optimization. Polyhedra and efficiency. Vols. A-C, Algorithms and Combinatorics, 24, A-C, Springer-Verlag, Berlin, 2003. MR 2004b:90004a, MR 2004b:90004b, MR 2004b:90004c

Review Information:

Reviewer: Alexander Barvinok
Affiliation: University of Michigan, Ann Arbor
Journal: Bull. Amer. Math. Soc. 41 (2004), 395-400
MSC (2000): Primary 90-02, 52-02; Secondary 90C27, 90C46, 52B20, 52B40, 91B52, 91B54
Published electronically: March 12, 2004
Review copyright: © Copyright 2004 American Mathematical Society
American Mathematical Society