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Volume 47, Number 1, 2003
Mathematical Sciences at 40 |
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Table of contents:
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This article:
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On greedy algorithms, partially ordered sets, and submodular functions - References
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by
B. L. Dietrich and A. J. Hoffman
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References
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G. Monge, “Déblai et Remblai,”
Mem. de l'Academie des Sciences (1781).
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F. L. Hitchcock, “The Distribution of a Product from Several Sources to Numerous Localities,”
J. Math. Phys. 20, 224–230 (1941).
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A. J. Hoffman, “On Simple Linear Programming Problems,”
Convexity: Proceedings of the Seventh Symposium in Pure Mathematics, V. Klee, Ed.,
Proceedings of Symposia in Pure Mathematics, Vol.
7, American Mathematical Society, Providence, RI,
1963, pp. 317–327.
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R. E. Burkard, B. Klinz, and R. Rodolf, “Perspectives of Monge Properties in Optimization,”
Discrete Appl. Math. 70, 95–161 (1996).
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J. Edmonds, “Matroids and the Greedy Algorithm,”
Math. Program. 1, 127–136 (1971).
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J. W. Gaddum, A. J. Hoffman, and D. Sokolowsky, “On the Solution to the Caterer Problem,”
Nav. Res. Logist. Quart. 1, 223–229 (1954).
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W. Jacobs, “The Caterer Problem,”
Nav. Res. Logist. Quart. 1, 154–165 (1954).
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A. J. Hoffman, “On Greedy Algorithms That Succeed,”
Surveys in Combinatorics, I. Anderson, Ed., Cambridge University Press, Cambridge, England,
1985, pp. 97–112.
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W. W. Bein, P. Brucker, J. K. Park, and P. K. Pathak, “A Monge Property for the d-Dimensional Transportation Problem,”
Discrete Appl. Math. 58,
97–109 (1995).
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M. Queyranne, F. Spieksma, and F. Tardella, “A General Class of Greedily Solvable Linear Programs,”
Math. Oper. Res. 23, 892–908 (1998).
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U. Faigle and W. Kern, “Submodular Linear Programs on Forests,”
Math. Program. 72, 195–206 (2000).
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U. Faigle and W. Kern, “On the Core of Ordered Submodular Cost Games,”
Math. Program. 87, Ser. A, 483–489 (2000).
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S. Fujishige, “A Note on Faigle and Kern's Dual Greedy Polyhedra,”
Math. Program. 88, Ser. A, 217–220 (2000).
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H. Gröflin and A. J. Hoffman, “Lattice Polyhedra II: Construction and Examples,”
Ann. Discrete Math. 15, 189–203 (1982).
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A. J. Hoffman and D. E. Schwartz, “On Lattice Polyhedra,”
Proceedings of the 5th Hungarian Conference in Combinatorics, A. Hajnal and V. T. Sos, Eds., 1976, North-Holland, Amsterdam,
1978, pp. 593–598.
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A. J. Hoffman, “On Lattice Polyhedra III, Blockers and Anti-blockers of Lattice Clusters,”
Polyhedral Combinatorics, Math. Programming Stud. 8, 197–207 (1978).
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W. W. Bein, P. Brucker, and A. J. Hoffman, “Series Parallel Composition of Greedy Linear Programming Problems,”
Math. Program. 62, Ser. B, 1–14 (1993).
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D. M. Topkis, “Minimizing a Submodular Function on a Lattice,”
Oper. Res. 26, 305–321 (1978).
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