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Book Review
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Book Information
Author(s):
S. Fujishige
Title:
Submodular functions and optimization theory
Additional book information:
Annals of Discrete Mathematics, no. 47, North Holland, Amsterdam, 270 pp., 1991, US$97.25. ISBN 0-444-88556-0
References:
- *
- O. Bondareva (1962), The core of an N-person game, Vestnik Leningrad Univ. 17, 141--142.
- *
- I. Curiel, G. Pederzoli, and S. Tijs (1989), Sequencing games, European J. Operational Res. \textbf{40}, 344--351.
- *
- J. Edmonds (1970), \emph{Submodular functions, matroids, and certain polyhedra}, Gordon and Breach, New York.
- *
- J. Edmonds and R. Giles (1977), A min-max relation for submodular functions on graphs, Ann. of Discrete Math. vol. 1, North-Holland, Amsterdam, 185--204.
- *
- A. Federgruen and H. Groenevelt (1988), Characterization and optimization of achievable performance in general queueing systems, Operations Res. \textbf{36}, 733--741.
- *
- A. Frank (1982), \emph{An algorithm for submodular functions on graphs\RM , \RM {(A. Bachem, M. Gr\"otschel, and B. Korte, eds.)}}, North-Holland, Amsterdam pp.~189--212.
- *
- D. Granot and M. Hojati (1990), On cost allocation in communication networks, Networks \textbf{20}, 209--229.
- *
- D. Granot and G. Huberman (1981), Minimum cost spanning tree games, Math. Programming \textbf{21}, 1--18.
- *
- D. Granot and G. Huberman (1981), The relationship between convex games and minimal cost spanning tree games\,\RM : a case for permutationally convex games, SIAM J. Algebra Discrete Math. \textbf{3}, 288--292.
- *
- H. Groenevelt (1985), \emph{Two algorithms for maximizing a separable concave function over a polymatroid feasible region}.
- *
- T. Ichiishi (1981), Supermodularity\,\RM : applications to convex games and to the greedy algorithm for LP, J. Economic Theory \textbf{25}, 283--286.
- *
- T. Ichiishi (1981), Comparative cooperative game theory, Internat. J. Game Theory \textbf{19}, 139--152.
- *
- L. Qi (1988), Odd submodular functions, Dilworth functions and discrete convex functions, Math. Oper. Res. \textbf{13}, 435--446.
- *
- R. T. Rockafellar (1970), Convex analysis, Princeton Univ. Press, Princeton, NJ.
- *
- D. Schmeidler (1972), Cores of exact games, J. Math. Anal. Appl. \textbf{40}, 214--225.
- *
- L. S. Shapley (1967), On balanced sets and cores, Naval Res. Logistics Quart. \textbf{14}, 453--460.
- *
- W. W. Sharkey (1982), Cooperative games with large cores, Internat. J. Game Theory \textbf{11}, 175--182.
- *
- R. Weber (1988), \emph{Probabilistic values for games} (A. Roth, ed.), Cambridge Univ. Press, Cambridge.
Additional Information:
Reviewer(s):
Richard P. McLean and William W.
Sharkey
Review Information:
Journal:
Bull. Amer. Math. Soc.
29
(1993),
98-104.
DOI:
10.1090/S0273-0979-1993-00387-2
PII:
S 0273-0979(1993)00387-2
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