What can geometry contribute to the study and understanding of linear programs and of the simplex algorithm? This little survey attempts to sketch a variety of answers to this question: We want to show that geometry and geometric insights
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474
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Linear Programming and Extensions
– Dantzig
- 1963
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176
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Convex polytopes
– Grunbaum
- 1967
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122
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A subexponential bound for linear programming
– Matouˇsek, Sharir, et al.
- 1996
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103
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How good is the simplex algorithm
– Klee, Minty
- 1972
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65
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A subexponential randomized simplex algorithm
– Kalai
- 1992
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37
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The Simplex Method: A Probabilistic Analysis
– Borgwardt
- 1987
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30
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A quasi-polynomial bound for the diameter of graphs of polyhedra
– Kalai, Kleitman
- 1992
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29
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The d−step conjecture and its relatives
– Klee, Kleinschmidt
- 1987
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21
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The numbers of faces of simplicial polytopes
– McMullen
- 1971
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19
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A Bad Network Problem for the Simplex Method and Other Minimum Cost Flow Algorithms
– Zadeh
- 1973
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17
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Randomized simplex algorithms on Klee-Minty cubes
– Gärtner, Ziegler
- 1994
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13
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The d-step conjecture for polyhedra of dimension d ! 6
– Klee, Walkup
- 1967
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13
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Lower bounds for a subexponential optimization algorithm
– Matousek
- 1994
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11
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Deformed products and maximal shadows
– Amenta, Ziegler
- 1998
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9
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Many polytopes meeting the conjectured Hirsch bound
– Holt, Klee
- 1998
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9
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Comonotone curves and polyhedra
– Motzkin
- 1957
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8
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Combinatorial linear programming: Geometry can help
– Gartner
- 1998
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7
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The monotonic bounded Hirsch conjecture is false for dimension at least 4
– Todd
- 1980
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6
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Polymake: A software package for analyzing convex polytopes. http://www.math.tu-berlin.de/diskregeom/polymake
– Gawrilow, Joswig
- 1998
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5
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Counterexamples to the strong d-step conjecture for d 5, Discrete Comput. Geometry 19
– Holt
- 1998
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5
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C.: Convex Polytopes
– unbaum, Klee, et al.
- 1967
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4
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On the complexity of the simplex algorithm, in: Advances in optimization and numerical analysis
– Goldfarb
- 1992
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3
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A framework for analyzing convex polytopes
– Polymake
- 2000
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1
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Zweidimensionale Projektionen von linearen Programmen
– Fischer
- 1998
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1
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polytopes meeting the conjectured Hirsch bound, Discrete Comput. Geometry 20
– Many
- 1998
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1
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On the monotone upper bound problem, in preparation
– Kaibel, Pfei, et al.
- 2002
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1
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no evil. Much of the raunchy porn on the internet wouldn't exist were it not for the help of a handful of legitimate companies operating quietly in the background
– Lubove, See
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1
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Die Probleme von Zadeh zum Netzwerk-Simplex sind deformierte Produkte von Polytopen
– Morstein
- 1999
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1
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Schwierige lineare Programme fur den Simplex-Algorithmus
– Schultz
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1
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The random-edge simplex algorithm on threedimensional polytopes, in preparation
– Sharir, Ziegler
- 2002
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1
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Kombinatorische Analyse einiger linearer Programme
– Weber
- 1999
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