On greedy algorithms, partially ordered sets, and submodular functions

IBM Journal of Research and Development

Volumn 47, Issue 1, 2003, Pages 25-30

  Dietrich, B L ^a   Hoffman, A J ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMBINATORIAL MATHEMATICS; FUNCTIONS; LINEAR PROGRAMMING; PROBLEM SOLVING; SET THEORY; TREES (MATHEMATICS);

GREEDY ALGORITHM; SUBMODULAR FUNCTIONS;

ALGORITHMS;

EID: 0037235118     PISSN: 00188646     EISSN: None     Source Type: Journal    
DOI: 10.1147/rd.471.0025     Document Type: Article

References (18)

1. G. Monge, "Déblai et Remblai," Mem. de l'Academie des Sciences (1781).
2. F. L. Hitchcock, "The Distribution of a Product from Several Sources to Numerous Localities," J. Math. Phys. 20, 224-230 (1941).
3. 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.
4. R. E. Burkard, B. Klinz, and R. Rodolf, "Perspectives of Monge Properties in Optimization," Discrete Appl. Math. 70, 95-161 (1996).
5. J. Edmonds, "Matroids and the Greedy Algorithm," Math. Program. 1, 127-136 (1971).
6. J. W. Gaddum, A. J. Hoffman, and D. Sokolowsky, "On the Solution to the Caterer Problem," Nav. Res. Logist. Quart. 1, 223-229 (1954).
7. W. Jacobs, "The Caterer Problem," Nav. Res. Logist. Quart. 1, 154-165 (1954).
8. A. J. Hoffman, "On Greedy Algorithms That Succeed," Surveys in Combinatorics, I. Anderson, Ed., Cambridge University Press, Cambridge, England, 1985, pp. 97-112.
9. 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).
10. M. Queyranne, F. Spieksma, and F. Tardella, "A General Class of Greedily Solvable Linear Programs," Math. Oper. Res. 23, 892-908 (1998).
11. U. Faigle and W. Kern, "Submodular Linear Programs on Forests," Math. Program. 72, 195-206 (2000).
12. U. Faigle and W. Kern, "On the Core of Ordered Submodular Cost Games," Math. Program. 87, Ser. A, 483-489 (2000).
13. S. Fujishige, "A Note on Faigle and Kern's Dual Greedy Polyhedra," Math. Program. 88, Ser. A, 217-220 (2000).
14. H. Gröflin and A. J. Hoffmann, "Lattice Polyhedra II: Construction and Examples," Ann. Discrete Math. 15, 189-203 (1982).
15. 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.
16. A. J. Hoffman, "On Lattice Polyhedra III, Blockers and Anti-blockers of Lattice Clusters," Polyhedral Combinatorics, Math. Programming Stud. 8, 197-207 (1978).
17. 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).
18. D. M. Topkis, "Minimizing a Submodular Function on a Lattice," Oper. Res. 26, 305-321 (1978).