Forward computation of dynamic slices is necessary to support interactive debugging and online analysis of long running programs. However, the overhead of existing forward computing algorithms limits their use to nonprocessing intensive applications. Recent empirical studies have shown that slices tend to reoccur often during execution. This paper presents a new forward computing algorithm for dynamic slicing, which is based on the stronger assumption that the same set union operations need to be performed repeatedly during slice computation. We present the results of an empirical study contrasting the performance of our new algorithm to the performance of a basic forward computing algorithm that unconditionally merges slices influencing an executing statement. The results indicate that the new algorithm is substantially faster than the basic algorithm and often requires significantly less memory.