MapReduce is commonly used as a parallel massive data processing model. When deploying it as a service over the open systems, the computational integrity of the participants is becoming an important issue due to the untrustworthy workers. Current duplication-based solutions can effectively solve non-collusive attacks, yet most of them require a centralized worker to re-compute additional sampled tasks to defend collusive attacks, which makes the worker a bottleneck. In this paper, we try to explore a trusted worker scheduling framework, named VAWS, to detect collusive attackers and assure the integrity of data processing without extra re-computation. Based on the historical results of verification, we construct an Integrity Attestation Graph (IAG) in VAWS to identify malicious mappers and remove them from the framework. To further improve the efficiency of identification, a verification-couple selection method with the IAG guidance is introduced to detect the potential accomplices of the confirmed malicious worker. We have proven the effectiveness of our proposed method on the improvement of system performance in theoretical analysis. Intensive experiments show the accuracy of VAWS is over 97% and the overhead of computation is closed to the ideal value of 2 with the increasing of the number of map tasks in our scheme.