An Exponential Lower Bound for the Parity Game Strategy Improvement Algorithm as We Know it

This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to V¨oge and Jurdzi´nski. First, we informally show which structures are difficult to solve for the algorithm. Second, we outline a family of games on which the algorithm requires exponentially many strategy iterations, answering in the negative the long-standing question whether this algorithm runs in polynomial time. Additionally we note that the same family of games can be used to prove a similar result w.r.t. the strategy improvement variant by Schewe as well as the strategy iteration for solving discounted payoff games due to Puri.

• Type: Conference
• Year: 2009
• Where: LICS
• Authors: Oliver Friedmann
• Keywords: Computer Science, LICS 2009, Strategy Improvement Algorithm, Strategy Improvement Variant, Strategy Iteration