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On a CMP (Chip Multi-Processor) architecture, cache sharing impacts threads non-uniformly, where some threads may be slowed down significantly, while others are not. This may cause severe performance problems such as throughput decreasing, cache thrashing. This paper proposes an architectural support predicting method (ASPM) to predict inter-thread cache contention, and schedules threads based on the results of the predicting on the CMP architecture. The architectural support consists of novel tagging which is remembering each cache line's interval time of reaccessing. The ASPM is very little loss of accuracy basis at low overhead (<;1%). We use this method for CMP scheduling, and find the performance is improving 9% on average.