Most algorithms for handling distributed deadlock problem in the generalized request model use the diffusing computation technique where propagation of probes and backward propagation of replies carrying dependency information between processes are both required to detect deadlock Since fast deadlock detection is critical, we propose an algorithm that lets probes rather than replies carry the information required for deadlock detection. This helps to remove the backward propagation of replies and reduce the time cost for deadlock detection to almost half of that of the existing algorithms. Moreover, the proposed algorithm is extended to deal with concurrent executions, which achieves further improvement of deadlock detection time, whereas the current algorithms deal only with a single execution. We compare the performance of the proposed algorithm with that of the other algorithms through simulation experiments.