  The problem of solving a parity game is at the core of many problems in model
checking, satisfiability checking and program synthesis. Some of the best
algorithms for solving parity game are strategy improvement algorithms. These
are global in nature since they require the entire parity game to be present at
the beginning. This is a distinct disadvantage because in many applications one
only needs to know which winning region a particular node belongs to, and a
witnessing winning strategy may cover only a fractional part of the entire game
graph.
  We present a local strategy improvement algorithm which explores the game
graph on-the-fly whilst performing the improvement steps. We also compare it
empirically with existing global strategy improvement algorithms and the
currently only other local algorithm for solving parity games. It turns out
that local strategy improvement can outperform these others by several orders
of magnitude.
