
Analysis of Lower Bounds for Simple Policy Iteration
Policy iteration is a family of algorithms that are used to find an opti...
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Tight running times for minimum ℓ_qnorm load balancing: beyond exponential dependencies on 1/ε
We consider a classical scheduling problem on m identical machines. For ...
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Aiming Low Is Harder  Inductive Proof Rules for Lower Bounds on Weakest Preexpectations in Probabilistic Program Verification
We present a new inductive proof rule for reasoning about lower bounds o...
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Solving Simple Stochastic Games with few Random Nodes faster using Bland's Rule
The best algorithm so far for solving Simple Stochastic Games is Ludwig'...
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Optimal Cost Almostsure Reachability in POMDPs
We consider partially observable Markov decision processes (POMDPs) with...
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Robust Exponential Worst Cases for DivideetImpera Algorithms for Parity Games
The McNaughtonZielonka divide et impera algorithm is the simplest and m...
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On Optimal Solutions to Compound Statistical Decision Problems
In a compound decision problem, consisting of n statistically independen...
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An Exponential Lower Bound for Zadeh's pivot rule
The question whether the Simplex Algorithm admits an efficient pivot rule remains one of the most important open questions in discrete optimization. While many natural, deterministic pivot rules are known to yield exponential running times, the randomfacet rule was shown to have a subexponential running time. For a long time, Zadeh's rule remained the most prominent candidate for the first deterministic pivot rule with subexponential running time. We present a lower bound construction that shows that Zadeh's rule is in fact exponential in the worst case. Our construction is based on a close relation to the Strategy Improvement Algorithm for Parity Games and the Policy Iteration Algorithm for Markov Decision Processes, and we also obtain exponential lower bounds for Zadeh's rule in these contexts.
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