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» On the Worst-case Complexity of Integer Gaussian Elimination
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ISSAC
1997
Springer
157views Mathematics» more  ISSAC 1997»
13 years 9 months ago
On the Worst-case Complexity of Integer Gaussian Elimination
Gaussian elimination is the basis for classical algorithms for computing canonical forms of integer matrices. Experimental results have shown that integer Gaussian elimination may...
Xin Gui Fang, George Havas
MP
2007
95views more  MP 2007»
13 years 4 months ago
Smoothed analysis of integer programming
We present a probabilistic analysis of integer linear programs (ILPs). More specifically, we study ILPs in a so-called smoothed analysis in which it is assumed that first an adve...
Heiko Röglin, Berthold Vöcking
IPCO
2007
126views Optimization» more  IPCO 2007»
13 years 6 months ago
The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
Abstract. A well established heuristic approach for solving various bicriteria optimization problems is to enumerate the set of Pareto optimal solutions, typically using some kind ...
René Beier, Heiko Röglin, Berthold V&o...
FCSC
2008
88views more  FCSC 2008»
13 years 4 months ago
Fraction-free matrix factors: new forms for LU and QR factors
Gaussian elimination and LU factoring have been greatly studied from the algorithmic point of view, but much less from the point view of the best output format. In this paper, we g...
Wenqin Zhou, David J. Jeffrey