<p><b>Abstract</b>—The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTIS-Mesh. The diameter of an <it>N</it><super>2</super>-processor OTIS-Mesh is <tmath>$4\sqrt N-3.$</tmath> We present an algorithm for routing any partial permutation in <tmath>$4\sqrt N+o\left( {\sqrt N} \right)$</tmath> time. Our selection algorithm runs in time <tmath>$6\sqrt N+o\left( {\sqrt N} \right)$</tmath> and our sorting algorithm runs in <tmath>$8\sqrt N+o\left( {\sqrt N} \right)$</tmath> time. All these algorithms are randomized and the stated time bounds hold with high probability. Also, the queue size needed for these algorithms is <it>O</it>(1) with high probability.</p>