6 l6LlOGRAPNY
This bibliography, which is a continuation of that in Volume I,‘ is arranged under
three headings:
IX.
X.
XI.
Theory of Graphs and Their Applications
Dynamic Programming
Theory of Games of Strategy
The following abbreviations are used:
J.O.R.S.A., Journal of the Operations Research Society of America (U.S.A.).
N.R.L.Q., Naval Research Logistics Quarterly. Office of Naval Research (U.S.A.).
Rand Report, Rand Corporation, Santa-Monica (U.S.A.).
O.R.Q., Operations Research Quarterly (Great Britain).
R.R.O., Revue de Recherche Operationelle (France).
B.C.R.O., Bolletino del Centro per la Ricerca Operativa (Italy).
C.C.E.R.O., Cahiers du Centre #Etudes de Recherche Op6rationelle (Belgium).
J.S.I.A.M., Journal of Society for Industrial and Applied Mathematics (U.S.A.).
Manag. Sc., Management Science (U.S.A.).
IX. Theory of Graphs and Their Applications
1 . WORKS
HI.
H2.
H3.
H4.
H5.
H6.
H7.
H8.
H9.
G. Avondo-Bodino, Economic Applications of the Theory of Graphs, Gordon and
Breach, New York, 1962.
C. Berge, ThLorie des graphes et ses applications, Dunod, Paris, 1958.
C. Berge and A. Ghouila-Houri, Programmes,jeux et rheaux de transport, Dunod,
Paris, 1962.
M. Denis-Papin, R. Faure, and A. Kaufmann, Cours de calcul booliien applique‘,
Albin Michel, Paris, 1963.
F. Harary and R. 2. Norman, Graph theory as a mathematical model in social
science, Univ. of Michigan, 1953.
D. Konig, Theorie der Endlichen und Unendlichen Graphen, Akad. Verl. M.B.H.,
Leipzig, 1936; or Chelsea, New York, 1950.
K. Lewin, Principle of topological psychology, McGraw-Hill, New York, 1936.
A. Sainte-Lague, Avec des nombres et des lignes, Vuibert, Paris, 1943.
Proceedings of Symposia in Applied Mathematics, Vol. X , “Combinatorial anaIysis,”
A m . Math. SOC.
(1960).
’
English language edition: A. Kaufmann, Methods and Models of Operations Research.
Prentice-Hall, Englewood Cliffs, New Jersey, 1963.
473
474
BIBLIOGRAPHY
2. ARTICLES
H10. P. Appel, “Le problbme gtomttrique des dtblais et remblais,” Mem. sci. math.
27 (1928).
H I 1. R. Bellman, “Combinatorial Processes and Dynamic Programming,” Proc.
Symp. Appt. Math.-Combinatorial Analysis, p. 21 7, 1960.
H12. C. Berge, “Two theorems in graph theory,” Proc. Natl. Acad. Sci. 43, 842 (1957).
H13. C. Berge, Sur le couplage maximum d’un graphe,” C. R . Acad. Sci. 247, 258
(1958).
H14. C. Berge, “Sur I’kquivalence du problbme de transport gtntralist et du problbme
des rtseaux,” C. R . Acad. Sci. 251, 324 (1960).
H15. C. Berge, “Les problbmes de flot et de tension,” C.C.E.R.O. 3, 69 (1961).
H16. R. Bott and J. P. Mayberry, “Matrices and trees,” Economic Activity Analysis,
p. 391. Wiley, New York, 1954.
H17. P. Camion, “Quelques proprittts des chemins et des circuits hamiltoniens dans
la thtorie des graphes,” C.C.E.R.O. 2, 10 (1960).
H18. A. Charnes and W. W. Cooper, “Nonlinear network flows and convex programming
over incidence matrices,” N.R.L.Q. 5 , 231 (1958).
H19. G. B. Dantzig, “On the shortest route, through a network,” Manag. Sci. 6,
187 (1960).
H20. J. Ergkvary, “Matrixok kombinatorius tulajdonsagairo1,”Mat. Fiz. Lapok 16(1931).
H21. J. Errera, “Du coloriage des cartes,” Thesis, Brussels, 1921; Mathesis 36, 56
(1922).
H22. C. Flament, “Nombre de cycles complets dans un rtseau de communications,”
Bull. centre itudes et recherches psychotechniques 3 (1959).
H23. C. Flament, “Analyse des structures prtftrentielles intransitives,” Proc. of the
Second Inter. Conf. of O.R., London, p. 150, 1960.
H24. M. M. Flood, “The travelling salesman problem,” J.O.R.S.A. 4, 61 (1956).
H25. M. M. Flood, “An alternating proof of a theorem of Konig as an algorithm for
Hitchcock distribution problem-10th on Applied Math.,” Am. Math. SOC.1960.
H26. L. R. Ford and D. R. Fulkerson, “Maximal flow through a network,” Canadian
J. Math. 8, 399 (1956).
H27. L. R. Ford and D. R. Fulkerson, “Dynamic network flow,” Rand Report, p. 967,
1956.
H28. L. R. Ford, “Network Flow Theory,” Rand Report, p. 923, 1956.
H29. L. R. Ford and D. R. Fulkerson, “A primal-dual algorithm for the capacited
Hitchcock problem,’’ Rand Report, p. 827, 1956.
H29a. D. Gale, “A Theorem on Flows in Network,” Paci’c J. Math. 7, 1073 (1957).
H30. V. D. Foulkes, “Directed graphes and assembly schedules,” Proc. Symp. Appl.
Math.-Combinatorial Analysis, p. 281, 1960.
H30a. G. de Ghellinck, “Aspects de la notion de dualitk en thtorie des graphes,”
C.C.E.R.O.3, 94 (1961).
H31, A. Ghouila-Houri, “Recherche du flot maximum dans certains rtseaux lorsqu’on
impose une condition de bouclage,” Proc. Second Intl. Conf. O.R., London,
p. 156, 1960.
H32. A. Ghouila-Houri, “Sur I’existence d’un flot ou d’une tension prenant ses valeurs
sur un groupe abklien,” C. R . Acad. Sci. 250, 3931 (1960).
H33. A. Ghouila-Houri, “Une gtntralisation de l’algorithme de Ford-Fulkerson,”
C. R . Acad. Sci. 250, 457 (1960).
H34. R. E. Gomory and T. C. Hu, “Multi-terminal networks,” I.B.M. Report R . C .
318, 1960.
IX. THEORY OF GRAPHS
475
H35. F. Harary and G. E. Uhlenbeck, “On some generalization of rooted trees,”
Abstract 131, Bull. Am. Math. SOC.58, 168 (1952).
H36. R. Kalaba, “On some communication network problems,” Proc. Symp. Appl.
Math.-Combinatorial analysis, p. 261, 1960.
H37. M. Kreweras, “Peut-on former un rCseau donnC avec des parties finies d’un
ensemble dCnombrable?,” C . R. Acad. Sci. 222, 1025 (1946).
H38. M. Kreweras, “Extension d’un theoreme sur les rtpartitions en classes,” C . R.
Acad. Sci. 222, 431 (1946).
H39. J. B. Kruskal, “On the shortest spanning subtree of a graph,” Proc. Am. Math.
SOC.7 , 48 (1956).
H40. H. J. Leavitt, “Some effect of certain communication patterns on groupe performance,” ]. Abnormal Social Psychol. 46, 28-50 (1951).
H41. S. MacLane, “A structural characterisation of planar combinatorial graphs,”
Duke Math. 1. 3, 466 (1937).
H42. D. G. Malcolm, J. H. Roseboom, C. E. Clark, and W. Fazar, “Application of a
technique for research and development program evaluation,” 1.O.R.S.A. 7 ,
646-669 (1959).
H43. Y. Malgrange, “PrCsentation d’un algorithme. Application B certains problbmes
de la thCorie des graphes,” Publication BULL. Utiliscltion des calculateurs dectroniques en R.O., 1961.
H44. G. Matthys and M. Ricard, “ h d e du dCbit maximal entre deux triages,” R.R.O.,
2nd ed., No. 15, 1960.
H45. G. Matthys, “Flow optimum dans un rCseau B capacitks de faisceaux,” Proc.
Second Intl. Conf. O.R., London, p. 164, 1960.
H46. Monge, “DCblai et remblai,” Mem. Acad. Sci. (1781).
H47. R. 2. Norman and M. 0. Rabin, “An algorithm for a minimum cover of a graph,”
Notices Am. Math. SOC.15, 193 (1891).
H48. S. Okada, ‘‘Algebraic and topological foundations of network synthesis,” Proc.
Symp. Modern Network Synthesis, p. 283, 1955.
H49. A. Orden, “The transshipment problem,” Manag. Sci. 2 (1956).
H50. J. PCtersen, “Die Theorie der regularen Graphs,” Acta Math. IS, 193
(1891).
H51. C. de Polignac, “ThCorie des ramifications,” Bull. SOC.Math. France 8, 120
( 1 880).
H52. M. Pollack and W. Wiebenson, “Solution of the shortest route problem (a
review),” J.O.R.S.A. 8, 224 (1960).
H53. G. Polya, “Sur le nornbre des isomeres de certains composts chimiques,” C. R.
Acad. Sci. 202, 1554 (1936).
H54. R. Radner and A. Tritter, “Communication in networks,” Cowles Comm. Paper,
2098, 1954.
H55. B. Roy, “Contribution de la thCorie des graphes B I’ttude de certains problemes
lintaires,” C . R. Acad. Sci. 248, 2437 (1959).
H56. B. Roy, “Cheminements et connexitk dans les graphes, application aux problbmes
d’ordonnancement,” Thtse, Paris, 1962.
H57. W. T. Tutte, “On Hamiltonian circuits,” 1.London Math. SOC.21, 99 (1946).
H58. H. Whitney, “Nonseparable and planar graphs,” Trans. Am. Math. SOC.34,
339 (1932).
H59. H. Whitney, “Congruent graphs and the connectivity of graphs,” Am. Math.
SOC.(1932).
H60. H. Whitney, “Planar graphs,” Fund. Math. 21, 73 (1933).
476
BIBLIOGRAPHY
X. Dynamic Programming
1. WORKS*
11.
12.
13.
14.
15.
16.
17.
18.
19.
110.
Ill.
R. Bellman, Dynamic Programming. Princeton Upiv. Press, Princeton, New Jersey,
1957.
R. Bellman, Adaptive Control Processes, a Guided Tour. Princeton Univ. Press,
Princeton, New Jersey, 1961.
R. Bellman and S. Dreyfus, Applied Dynamic Programming. Princeton Univ.
Press, Princeton, New Jersey, 1962.
A. T. Bharuche-Reid, Elements of the Theory of Markov Processes and their
Applications. McGraw-Hill, New York, 1960.
R. Companys, unpublished work.
R. Howard, Dynamic Programming and Markov Processes. Technology Press,
M I T , Wiley, New York, 1960.
Kai Lai Chung, Markov Chains with Stationary TransitionProbabilities. SpringerVerlag, Berlin, 1960.
A. Kaufmann and R. Cruon, La programmation dynamipue et ses applications.
Dunod, to appear.
P. Rosenstiehl and A. Ghouila-Houri, Les choix kconomiques. Decisions siquentielles
et simulation. Dunod, Paris, 1960.
Proceedings of Symposia in Applied Mathematics, Vol. X, Combinatorial analysis,
A m . Math. SOC.(1960).
J. C . Kemeny and J. L. Snell, Finite Markov Chains. Van Nostrand, Princeton,
New Jersey, 1960.
2. A W I C L E S
I l l a . R. Bellman, “The theory of dynamic programming,” Bull. A m . Math. Soc.
60, 503-515 (1954).
112. R. Bellman, “Equipment replacement policy,” J . S . I . A . M . 3, 133-1 36 (1955).
113. R. Bellman, “Dynamic programming and Lagrange multipliers,” Proc. N a d .
Acad. Sci. 42, 767-769 (1956).
114. R. Bellman, “On the application d the theory of dynamic programming to the
study of control processes, Pror. Symp. Control Processes, Polytechnic Institute
of Brooklyn, New York, p. 199-213 (1956).
115. R. Bellman, “Mathematical’ aspects of scheduling theory,” J.S.Z.A.M.4, 168-205
(1956).
116. R. Bellman, “On the theory of dynamic programming. A warehousing problem,”
Manag. Sci. 2, 272-276 (1956).
117. R. Bellman, “Dynamic programming and the smoothing problem,” Manag.
Sci. 3, 111-113 (1956).
118. R. Bellman, “On the computational solution of linear programming problems
involving almost block diagonal matrices,” Manag. Sci. 3, 403-406 (1957).
119. R. Bellman, “On the computational solution of dynamic programming processes.
On a cargo loading problem,” Rand Report R. M. 1746, 1956.
* I4 and I7 deal only with Markovian decision chains and processes. I10 contains
several sections on dynamic programming, and there are numerous references to the
subject in 11, 2, 3, 8, and 9.
XI. GAMES OF STRATEGY
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
477
R. Bellman, “On the computational solution of dynamic programming processes.
A smoothing problem, Rand Report R. M. 1749, 1957.
R. Bellman, “On the computational solution of dynamic programming processes.
The flyaway kit problem,” Rand Report R. M. 1889, 1957.
R. Bellman and R. Kalaba, “On the role of dynamic programming in statistical
communication theory,” Trans. I.R.E. IT-3, 197-203 (1957).
R. Bellman, “Dynamic programming and the reliability of multicomponent
devices,” J.O.R.S.A. 6 , 200-206 (1958).
R. Bellman, “Communication processes involving learning and random duration,”
Convention I.R.E. Information Theory, Part 4, pp. 16-20, 1958.
R. Bellman, “Dynamic programming and stochastic control processes,” Information and control l , 228-239 (1958).
R. Bellman, “Some new techniques in the dynamic programming solutions of
variational problems,” Quart. Appl. Math. 16, 295-305 (1958).
R. Bellman and Dreyfus, “An application of dynamic programming to the determination of optimal satellite trajectory problems,” /. British Interplanetary SOC.
17, 78-83 (1959).
R. Bellman and S. Dreyfus, “Functional approximation and dynamic programming,” Math. tables XIII, 247-251 (1959).
R. Bellman and R. Kalaba, “Reduction of dimensionality, Dynamic programming
and control processes,” Rand Report, p. 1694, 1960.
R. Beckwith, “Analytic and computational aspects of dynamic programming
processes of high dimension,” Thise, Purdere Univ., 1959.
L. Bosset, “RCsolution de certaines tquations en programmation dynamique.”
Siminaire d’Analyse numlrique de 1’A.F.C.A.L.T.I. (1960).
H. Cartaino and S. Dreyfus, “Applications of dynamic programming to the
minimum time-to-climb problem,” Aeronautical Engr. Rev. (1957).
M . Cuenod, “MCthode de calcul B I’aide de suites,” Sciences technique, P. Feissly,
Lausanne, 1955.
G. B. Dantzig, “On the status of multistage linear programming problems,”
Management Science 6 , No. 1 (1959).
S. Dreyfus, “A generalized equipment replacement study,” J.S.I.A.M. 8,
425-435 (1960).
F. d’Epenoux, “Sur un problkme de production et de stockage dans l’alCatoire,”
R.R.O. No. 14, 1960.
R. Fortet, “ProprittCs des applications de transition des programmations dynamiques,” Revue METRA, 11, No. 1, 79-97 (1963).
S. Johnson and S. Karlin, “A Bayes model in sequential design,” Ann. Math.
Stutut. ( 1956).
J. D. C. Little, “The use of storage water in a hydroelectric system,” J.O.R.S.A.
(1955).
XI. Theory of Games of Strategy
1. WORKS*
JI.
K. J. Arrow, “Social choice and individual values,” Cowles Comm. Res. Econ.
No. 12. Wiley, New York, 1951.
* The reader should also consult the bibliographies in 54, 7, 11, 15, 16, and 19.
478
J2.
J3.
14.
J5.
56.
J7.
JS.
J9.
JlO.
J11.
J12.
J13.
114.
Jl5.
116.
117.
118.
J19.
J20.
521.
122.
J23.
BIBLIOGRAPHY
K. J. Arrow, Mathematical Models in Social Sciences. Stanford Univ. Press,
Stanford, California, 1951.
C. Berge, The‘orie gek’rale des jeux a n personnes. Gauthier-Villars, Paris, 1957.
D. Blackwell and M. A. Girshick, Theory of Games and Statistical Decisions.
Wiley, New York, 1954.
T. Bonnessen and W. Fenchel, Theorie der convexen Korper. Springer Verlag,
Berlin, 1934; or Chelsea, New York, 1948.
Burger, Einfiihrung in die Theorie der Spiels. De Gruyter, 1960.
H. Chernoff and L. E. Moses, Elementary Decision Theory. Wiley, New York,
or Chapman and Hall, London, 1959.
J. R. Gaenne and R. L. Sisson, Dynamic Management and Decision Games. Wiley,
New York, 1959.
G. T. Guilbaud, “Stratkgies et dkcisions economiques,” C.N.R.S.
(1954).
Herbemont (d’), “Aspects de la thkorie statistique des dkcisions,” Informations
Scientifques, Bull. (1961).
S. P. Jacot, “Stratkgie et concurrence,” Thise, University of Lyon, 1961.
A. Kaufmann, R. Faure and A. Le Garff, Les jeux d’entreprises. Presses Univ.
de France (Collection Que sais-je ?), 1960.
T. C. Koopmans, Activity Analysis of Production and Allocations. Wiley, New
York, 1951.
H. W. Kuhn and A. W. Tucker, “Contribution to the theory of games,” Annals
of Mathematics Studies, Vols. I and 11. Princeton Univ. Press, Princeton, New
Jersey, 1950 and 1953.
R. D. Luce and H. Raiffa, Games and Decisions. Wiley, New York, 1957.
J. C. C. MacKinsey, A n Introduction to Theory of Games. McGraw-Hill, New
York, 1952.
J. von Neumann and 0. Morgenstern, Theory of Games and Economic Behavior.
Princeton Univ. Press, Princeton, New Jersey, 1953.
M. Shubik, Stratigie et structure des marche‘s. Dunod, Paris, 1963 (Strategy and
Market Structure. Wiley, New York, 1959).
P. M. Thrall, C. H. Coombs and R. L. Davis, Decision Processes. Wiley, New
York; or Cbapman and Hall, London, 1954.
S. Vajda, Thdorie des jeux et programmation Iine‘aire. Dunod, Paris, 1959 (The
Theory of Games and Linear Programming. Methuen, London; or Wiley, New
York, 1956).
A. Wald, Statistical Decision Functions. Wiley, New York, 1950.
L. Weiss, Statistical Decision Theory. McGraw-Hill, New York, 1961.
J. D. Williams, L a stratdgie duns les actions humaines. Dunod, Paris, 1956 (The
compleat Strategist. McGraw-Hill, New York, 1954).
2. ARTICLES
J24.
J25.
J26.
J27.
M. Allais, “Le comportement de l’homme rationnel devant le risque: critique
des postulats et axiomes de 1’Ccole amtricaine,” Econometrica 21, 503-546 (1953).
I
K. J. Arrow, “Alternative approaches to the theory of choice in risk-taking
situations,” Econometrica 19, 404-437 (1951).
K. J. Arrow, Hurwicz’s optimality criterion for decision-making under ignorance,”
Stanford Univ., Dept. of Economics and Statistics, Stanford, California, 1951.
T. Bayes, Facsimiles of two papers by Bayes prepared under the direction of
W. E. Deming, The Graduate School Dept. of Agriculture, Washington D.C.,
Pt. 16, 52 pp.
XI. GAMES OF STRATEGY
J28.
J29.
530.
J31.
532.
J33.
534.
J35.
536.
537.
J38.
J39.
J40.
541.
J42.
J43.
J44.
J45.
J46.
547.
J48.
549.
J50.
J5l.
J5l.
J52.
479
R. Bellman, “Decision making in the face of incertainty, N.R.L.Q. 1, 230-232
and 327-332 (1954).
D. Blackwell and M. A. Girshick, “Bayes and minimax solutions of sequential
decision problems,” Econometrica 17, 213-243 (1949).
G. B. Dantzig, “A proof of the equivalence of the programming problem and
the game problem,” Duns /. 13, 33G338 (1951).
G. B. Dantzig, “Constructive proof of the minimax theorem,” Pacific /. Math.
6, 25-33 (1956).
R. Dorfman, “Application of the simplex method to a game theory problem,”
Duns. J. 13, 348-358 (1951).
D. Gale, “Convex polyhedral cones and linear inequalities,” Duns. J. 13, 287-297
(1951).
D. Gale, H. W. Kuhn, and A. W. Tucker, “Reduction of games matrices,” Dans
J. 14, 89-99 (1950).
D. Gale, H. W. Kuhn, and A, W. Tucker, “Linear programming and the theory
of Games,” Duns. J. 13, 317-329 (1951).
D. Gale and S. Sherman, “Solutions of finite two-persons games,” Duns /. 14,
37-50 (1950).
D. Gale and F. M. Stewart, “Infinite game with perfect information,” Duns /.
14, 245-266 (1953).
M. Gerstenhaber, “Theory of convexe polyhedral cones,” Duns J. 13, 298-316
(1951).
I. N. Herstein and J. Milnor, “An axiomatic approach to measurable utility,”
Econometrica 21, 291-297 (1953).
L. Hprwicz, “A criterion for decision-making under incertainty,” Cowles Com.
Discus. Paper, Statistics, No. 355.
S. Karvn, !‘Continuous games,” Proc. Natl. Acud. Sci. USA 37, 220-223 (1951).
H. W. Kuhn, “Lectures on the theory of games. Logistic prof.” Office of Naval
Res., Princeton Univ. Press, Princeton, New Jersey, 1953.
R. D. Luce, “A definition of stability for n-persons game theory,” Math. models
of Human behaoior, Dunlap and Assoc., Stanford, California, 1955.
J. C. C. MacKinsey, “Isomorphism of games and strategic equivalence,” Duns
/. 14, 117-130 (1950).
J. Marschak and R. Radner, “Criteria for planning and incomplete information,”
Cowles Comm. Discuss. Paper, Economics, No. 2018, 1951.
J . Milnor, “Games against nature,” Duns /. 19 (1954).
J. F. Nash, “Equilibrium points in n-persons games,” Proc. Natl. Acad. Sci.
USA 36, 38-49 (1950).
L. J. Savage, “The theory of statistical decision,” /. Am. Stat. Ass. pp, 238-248,
1947.
M. Shubik, “Information, theories of competition, and the theory of games,”
J. Political Econ. 60, 145-150 (1952).
H. Weyl, “Elementary proof of a minimax theorem due to von Neumann,”
Duns J. 14, 19-25 (1950).
H. Weyl, “Elementary proof of a minimax theorem due to von Neumann,”
Duns /. 14, 19-25 (1950).
H. Weyl, “The elementary theory of convex polyhedra,” Duns /. 14,3-18 (1950).
“Colloques internationaux du Centre national de la Recherche Scientifique
(C.N.R.S.),” La dicision, i d . C.N.R.S., Paris, 1961.