  We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model
at the critical point. For the dynamic critical exponents associated to the
integrated autocorrelation times of the "energy-like" observables, we find
z_{int,N} = z_{int,E} = z_{int,E'} = 0.459 +- 0.005 +- 0.025, where the first
error bar represents statistical error (68% confidence interval) and the second
error bar represents possible systematic error due to corrections to scaling
(68% subjective confidence interval). For the "susceptibility-like"
observables, we find z_{int,M^2} = z_{int,S_2} = 0.443 +- 0.005 +- 0.030. For
the dynamic critical exponent associated to the exponential autocorrelation
time, we find z_{exp} \approx 0.481. Our data are consistent with the
Coddington-Baillie conjecture z_{SW} = \beta/\nu \approx 0.5183, especially if
it is interpreted as referring to z_{exp}.
