One of the most common optimistic synchronization protocols for parallel simulation is the Time Warp algorithm proposed by Jefferson . Time Warp algorithm is based on the virtual time paradigm that has the potential for greater exploitation of parallelism and, perhaps more importantly, greater transparency of the synchronization mechanism to the simulation programmer. It is widely believe that the optimistic Time Warp algorithm suffers from large memory consumption due to frequent rollbacks. In order to achieve optimal memory management, Time Warp algorithm needs to periodically reclaim the memory. In order to determine which event-messages have been committed and which portion of memory can be reclaimed, the computation of global virtual time (GVT) is essential. Mattern  uses a distributed snapshot algorithm to approximate GVT which does not rely on first in first out (FIFO) channels. Specifically, it uses ring structure to establish cuts C1 and C2 to calculate the GVT for distinguishing between the safe and unsafe event-messages. Although, distributed snapshot algorithm provides a straightforward way for computing GVT, more efficient solutions for message acknowledging and delaying of sending event messages while awaiting control messages are desired. This paper studies the memory requirement and time complexity of GVT computation. The main objective of this paper is to implement the concept of matrix with the original Mattern's GVT algorithm to speedups the process of GVT computation while at the same time reduce the memory requirement. Our analysis shows that the use of matrix in GVT computation improves the overall performance in terms of memory saving and latency.