Average case complete problems
SIAM Journal on Computing
Matching is as easy as matrix inversion
Combinatorica
Exact arborescences, matchings and cycles
Discrete Applied Mathematics
Probabilistic analysis of the multidimensional knapsack problem
Mathematics of Operations Research
Some perturbation theory for linear programming
Mathematical Programming: Series A and B
Linear programming, complexity theory and elementary functional analysis
Mathematical Programming: Series A and B
Exponentially small bounds on the expected optimum of the partition and subset sum problems
Random Structures & Algorithms
Average-case analysis of off-line and on-line knapsack problems
Journal of Algorithms - Special issue on SODA '95 papers
Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Smoothed analysis of the perceptron algorithm for linear programming
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Random knapsack in expected polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Average Case and Smoothed Competitive Analysis of the Multi-Level Feedback Algorithm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Probabilistic analysis of knapsack core algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Decision-making based on approximate and smoothed Pareto curves
Theoretical Computer Science
Average-Case and Smoothed Competitive Analysis of the Multilevel Feedback Algorithm
Mathematics of Operations Research
The diameter of randomly perturbed digraphs and some applications
Random Structures & Algorithms
Smoothed analysis: an attempt to explain the behavior of algorithms in practice
Communications of the ACM - A View of Parallel Computing
Settling the complexity of local max-cut (almost) completely
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Smoothed analysis of algorithms and heuristics
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Decision making based on approximate and smoothed pareto curves
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Smoothed analysis of integer programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
The smoothed analysis of algorithms
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We present a probabilistic analysis for a large class of combinatorial optimization problems containing, e. g., all binary optimization problems defined by linear constraints and a linear objective function over (0,1)n. By parameterizing which constraints are of stochastic and which are of adversarial nature, we obtain a semi-random input model that enables us to do a general average-case analysis for a large class of optimization problems while at the same time taking care for the combinatorial structure of individual problems. Our analysis covers various probability distributions for the choice of the stochastic numbers and includes smoothed analysis with Gaussian and other kinds of perturbation models as a special case. In fact, we can exactly characterize the smoothed complexity of optimization problems in terms of their random worst-case complexity.A binary optimization problem has a polynomial smoothed complexity if and only if it has a pseudopolynomial complexity. Our analysis is centered around structural properties of binary optimization problems, called winner, loser, and feasibility gaps. We show, when the coefficients of the objective function and/or some of the constraints are stochastic, then there usually exist a polynomial n-Ω(1) gap between the best and the second best solution as well as a polynomial slack to the boundary of the constraints. Similar to the condition number for linear programming, these gaps describe the sensitivity of the optimal solution to slight perturbations of the input and can be used to bound the necessary accuracy as well as the complexity for solving an instance. We exploit the gaps in form of an adaptive rounding scheme increasing the accuracy of calculation until the optimal solution is found. The strength of our techniques is illustrated by applications to various NP-hard optimization problems from mathematical programming, network design, and scheduling for which we obtain the the first algorithms with polynomial average-case/smoothed complexity.