A new polynomial-time algorithm for linear programming
Combinatorica
Theory of linear and integer programming
Theory of linear and integer programming
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A subexponential randomized simplex algorithm (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A survey of linear programming in randomized subexponential time
ACM SIGACT News
A Subexponential Algorithm for Abstract Optimization Problems
SIAM Journal on Computing
The worst-case running time of the random simplex algorithm is exponential in the height
Information Processing Letters
Linear programming, the simplex algorithm and simple polytopes
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Finite State Markovian Decision Processes
Finite State Markovian Decision Processes
The random facet simplex algorithm on combinatorial cubes
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
Random Structures & Algorithms
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
A randomized polynomial-time simplex algorithm for linear programming
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Understanding and Using Linear Programming (Universitext)
Understanding and Using Linear Programming (Universitext)
The Klee–Minty random edge chain moves with linear speed
Random Structures & Algorithms
Two New Bounds for the Random-Edge Simplex-Algorithm
SIAM Journal on Discrete Mathematics
An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Exponential lower bounds for policy iteration
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Lower bounds for a subexponential optimization algorithm
Random Structures & Algorithms
A subexponential lower bound for Zadeh's pivoting rule for solving linear programs and games
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
On the complexity of policy iteration
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A subexponential lower bound for Zadeh's pivoting rule for solving linear programs and games
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Polynomial-Time algorithms for energy games with special weight structures
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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The simplex algorithm is among the most widely used algorithms for solving linear programs in practice. With essentially all deterministic pivoting rules it is known, however, to require an exponential number of steps to solve some linear programs. No non-polynomial lower bounds were known, prior to this work, for randomized pivoting rules. We provide the first subexponential (i.e., of the form 2Ω(nα), for some α0) lower bounds for the two most natural, and most studied, randomized pivoting rules suggested to date. The first randomized pivoting rule considered is Random-Edge, which among all improving pivoting steps (or edges) from the current basic feasible solution (or vertex) chooses one uniformly at random. The second randomized pivoting rule considered is Random-Facet, a more complicated randomized pivoting rule suggested by Kalai and by Matousek, Sharir and Welzl. Our lower bound for the Random-Facet pivoting rule essentially matches the subexponential upper bounds given by Kalai and by Matousek et al Lower bounds for Random-Edge and Random-Facet were known before only in abstract settings, and not for concrete linear programs. Our lower bounds are obtained by utilizing connections between pivoting steps performed by simplex-based algorithms and improving switches performed by policy iteration algorithms for solving Markov Decision Processes (MDPs).