Input queued switches have been well studied in the recent past. A scheduling algorithm is required to schedule the transfer of packets through the switch fabric (e.g. crossbar) at every time slot. The maximum weight matching (MWM) algorithm is known to deliver 100% throughput under any admissible traffic. However, MWM is not practical for its high computational complexity O(N/sup 3/). In this paper, we study a class of approximation algorithms to MWM from the point of view of local search. Notably we observe that: (a) Local search is well suitable for parallel computation. (b) Each line card of high performance router has at least one processor. Based on the two important observations, a parallelized greedy scheduling algorithm is proposed. The proposed algorithm is proved to be rate stable under any admissible traffic. Simulation results show that our algorithm outperforms other randomized approximations to MWM.