Error Analysis and Correction for Weighted A*'s Suboptimality (Extended
  Version)
  Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally,
solving planning and search problems. The cost of the solution it produces is
guaranteed to be at most W times the optimal solution cost, where W is the
weight wA* uses in prioritizing open nodes. W is therefore a suboptimality
bound for the solution produced by wA*. There is broad consensus that this
bound is not very accurate, that the actual suboptimality of wA*'s solution is
often much less than W times optimal. However, there is very little published
evidence supporting that view, and no existing explanation of why W is a poor
bound. This paper fills in these gaps in the literature. We begin with a
large-scale experiment demonstrating that, across a wide variety of domains and
heuristics for those domains, W is indeed very often far from the true
suboptimality of wA*'s solution. We then analytically identify the potential
sources of error. Finally, we present a practical method for correcting for two
of these sources of error and experimentally show that the correction
frequently eliminates much of the error.
