Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Probabilistic analysis of the multidimensional knapsack problem
Mathematics of Operations Research
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Average saving effects in enumerative methods for solving knapsack problems
Journal of Complexity
Applying Lehman's theorems to packing problems
Mathematical Programming: Series A and B
The rank facets of the stable set polytope for claw-free graphs
Journal of Combinatorial Theory Series B
Average-case analysis of off-line and on-line knapsack problems
Journal of Algorithms - Special issue on SODA '95 papers
Split Closure and Intersection Cuts
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Clique family inequalities for the stable set polytope of quasi-line graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Probabilistic analysis of knapsack core algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Typical properties of winners and losers in discrete optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Random knapsack in expected polynomial time
Journal of Computer and System Sciences - Special issue: STOC 2003
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
A construction for non-rank facets of stable set polytopes of webs
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Smoothed analysis of binary search trees
Theoretical Computer Science
The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Smoothed analysis: an attempt to explain the behavior of algorithms in practice
Communications of the ACM - A View of Parallel Computing
The smoothed analysis of algorithms
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
On the feedback vertex set polytope of a series-parallel graph
Discrete Optimization
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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 adversary specifies the coefficients of an integer program and then (some of) these coefficients are randomly perturbed, e.g., using a Gaussian or a uniform distribution with small standard deviation. In this probabilistic model, we investigate structural properties of ILPs and apply them to the analysis of algorithms. For example, we prove a lower bound on the slack of the optimal solution. As a result of our analysis, we are able to specify the smoothed complexity of classes of ILPs in terms of their worst case complexity. For example, we obtain polynomial smoothed complexity for packing and covering problems with any fixed number of constraints. Previous results of this kind were restricted to the case of binary programs.