Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time

Authors:
Daniel Spielman;Shang-Hua Teng
Affiliations:
Department of Mathematics, M.I.T., Cambridge, MA;Akamai Technologies Inc. and Department of Computer Science, University of Illinois at Urbana-Champaign
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

Citing 6
Cited 26

A new polynomial-time algorithm for linear programming

Combinatorica
A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension

Journal of the ACM (JACM)
Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm

Mathematical Programming: Series A and B
Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems

Mathematical Programming: Series A and B
A simplex variant solving an m×d linear program in O(min(m2,d2)) expected number of pivot steps

Journal of Complexity
A subexponential randomized simplex algorithm (extended abstract)

STOC '92 Proceedings of the twenty-fourth 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
Visual exploration and incremental utility elicitation

Eighteenth national conference on Artificial intelligence
Random knapsack in expected polynomial time

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Typical properties of winners and losers in discrete optimization

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Mechanism design for policy routing

Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Random knapsack in expected polynomial time

Journal of Computer and System Sciences - Special issue: STOC 2003
A yield improvement methodology using pre- and post-silicon statistical clock scheduling

Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Statistical timing analysis driven post-silicon-tunable clock-tree synthesis

ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
The diameter of randomly perturbed digraphs and some applications

Random Structures & Algorithms
Coalition Formation: From Software Agents to Robots

Journal of Intelligent and Robotic Systems
Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms

Random Structures & Algorithms
How many random edges make a dense hypergraph non-2-colorable?

Random Structures & Algorithms
Expansion and Lack Thereof in Randomly Perturbed Graphs

Algorithms and Models for the Web-Graph
Backdoors to typical case complexity

IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Adaptive resource allocation for service-based systems

Proceedings of the First Asia-Pacific Symposium on Internetware
Adaptive Performance Management for SMS Systems

Journal of Network and Systems Management
Linear programming

Algorithms and theory of computation handbook
Why large CLOSEST STRING instances are easy to solve in practice

SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
On the complexity of the metric TSP under stability considerations

SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Worst-case and average-case approximations by simple randomized search heuristics

STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On trip planning queries in spatial databases

SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Searching Steiner trees for web graph query

Computers and Industrial Engineering
Intuitive algorithms and t-vertex cover

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The effectiveness of lloyd-type methods for the k-means problem

Journal of the ACM (JACM)
A framework for evaluating the smoothness of data-mining results

ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Storage optimization for 3D streaming systems

Proceedings of the 5th ACM Multimedia Systems Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. Essentially, we study the performance of algorithms under small random perturbations of their inputs. We show that the shadow-vertex simplex algorithm has polynomial smoothed complexity.