  This paper presents a new lower bound for the discrete strategy improvement
algorithm for solving parity games due to Voege and Jurdziski. First, we
informally show which structures are difficult to solve for the algorithm.
Second, we outline a family of games of quadratic size 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.
