Input Queued switches have been very well studied in the recent past. 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(N3 ). In this paper, we study a class of approximations to MWM from the point of view of local search. Firstly, we propose a greedy scheduling algorithm called GSA. It has the following features: (a) It is very simple to compute the weight of a neighbor matching. GSA only needs to compute the weight of two swapped edges instead of the weight of all the edges. (b) The computational complexity of GSA is O(c_max), where c_max denotes the maximum number of iterations. Hence we can adjust the value of c_max to achieve low computational complexity. Secondly, we observe that: (a) Local search is well suitable for parallel computing. (b) Each line card of high performance router has at least one processor. Based on the two important observations, w...