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35th Annual Symposium on Foundations of Computer Science (FOCS 1994)
Santa Fe, NM, USA
November 20November 22
ISBN: 0818665807
ASCII Text  x  
B. Gartner, G.M. Ziegler, "Randomized simplex algorithms on KleeMinty cubes," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 502510, 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), 1994.  
BibTex  x  
@article{ 10.1109/SFCS.1994.365741, author = {B. Gartner and G.M. Ziegler}, title = {Randomized simplex algorithms on KleeMinty cubes}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {1994}, isbn = {0818665807}, pages = {502510}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1994.365741}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Randomized simplex algorithms on KleeMinty cubes SN  0818665807 SP502 EP510 A1  B. Gartner, A1  G.M. Ziegler, PY  1994 KW  quadratic worstcase behavior KW  randomized simplex algorithms KW  KleeMinty cubes KW  linear programs KW  combinatorial models KW  quadratic lower bounds KW  complexity KW  quadratic upper bounds VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes (1972) and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same lime, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worstcase behavior on general linear programs.
Index Terms:
quadratic worstcase behavior, randomized simplex algorithms, KleeMinty cubes, linear programs, combinatorial models, quadratic lower bounds, complexity, quadratic upper bounds
Citation:
B. Gartner, G.M. Ziegler, "Randomized simplex algorithms on KleeMinty cubes," focs, pp.502510, 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), 1994
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