Value-flow analysis is a fundamental technique in program analysis, benefiting various clients, such as memory corruption detection and taint analysis. However, existing efforts suffer from the low potential speedup that leads to a deficiency in scalability. In this work, we present a parallel algorithm Octopus to collect path conditions for realizable paths efficiently. Octopus builds on the realizability decomposition to collect the intraprocedural path conditions of different functions simultaneously on-demand and obtain realizable path conditions by concatenation, which achieves a high potential speedup in parallelization. We implement Octopus as a tool and evaluate it over 15 real-world programs. The experiment shows that Octopus significantly outperforms the state-of-the-art algorithms. Particularly, it detects NULL-pointer-dereference bugs for the project llvm with 6.3 MLoC within 6.9 minutes under the 40-thread setting. We also state and prove several theorems to demonstrate the soundness, completeness, and high potential speedup of Octopus . Our empirical and theoretical results demonstrate the great potential of Octopus in supporting various program analysis clients. The implementation has officially deployed at Ant Group, scaling the nightly code scan for massive FinTech applications.