In terms of program verification data-flow analysis (DFA) is commonly understood as the computation of the strongest postcondition for every program point with respect to a precondition which is assured to be valid at the entry of the program. Here, we consider DFA under the dual weakest precondition view of program verification. Based on this view we develop an approach for demand-driven DFA of explicitly parallel programs, which we exemplify for the large and practically most important class of bitvector problems. This approach can directly be used for the construction of online debugging tools. Moreover, it is tailored for parallelization. For bitvector problems, this allows us to compute the information provided by conventional, strongest postcondition-centered DFA at the costs of answering a data-flow query, which are usually much smaller. In practice, this can lead to a remarkable speed-up of analysing and optimizing explicitly parallel programs.