Snapshot Isolation (SI) is a widely adopted concurrency control mechanism in database systems, which utilizes timestamps to resolve conflicts between transactions. However, centralized allocation of timestamps is a potential bottleneck for parallel transaction management. This bottleneck is becoming increasingly visible with the rapidly growing degree of parallelism of today's computing platforms. This paper introduces Posterior Snapshot Isolation (PostSI), an SI mechanism that allows transactions to determine their timestamps autonomously, without relying on centralized coordination. As such, PostSI can scale well, rendering it suitable for various multi-core and MPP platforms. Extensive experiments are conducted to demonstrate its advantage over existing approaches.