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In this paper, We consider the problem of sorting n2 numbers, initially distributed randomly in an n × n mesh-connected processor array with one element per processor. We show a lower bound, based on distance arguments, of 4n routing steps on mesh-connected processors operating in an SIMD mode with no wraparounds in rows or columns, We present an algorithm using a novel approach, which is optimal upto the conslant of the leading term, and hence, succeed in proving the tightness of the lower bound based on distance. Keeping in mind the practical difficulties in implementation of this algorithm, we also present an extremely practical O(n) algorithm amenable for VLSI implementation and for existing mesh- connected computers. All the results in this paper were derived by using a new method of analysis inspired by the discovery of shear-sort or row-column sort.