Before revision:   A local algorithm, as defined by Rubinfeld et al. (ICS 2011), for constructing a spanning subgraph with almost minimum weight, specifically, at most a factor (1+\epsilon) of the optimum, with poly(1/\epsilon)-query complexity.
After revision:  (2) A local algorithm, as defined by Rubinfeld et al. (ICS 2011), for constructing a spanning subgraph with almost minimum weight, specifically, at most a factor (1+\epsilon) of the optimum, with poly(1/\epsilon)-query complexity.