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Vertical stacking of multiple optical banyan networks is a novel scheme for building banyan-based nonblocking optical switches. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves the properties of small depth and absolutely loss uniformity but loses the nice self-routing capability of banyan networks. To guarantee a high switching speed, routing in VSOB network needs special attentions so that paths can be established as fast as possible. The best known global routing algorithm for an N×N nonblocking VSOB network has the time complexity of O(NlogN), which will introduce an unacceptable long delay in path establishment for a large size optical switch. In this paper, we propose two fast routing algorithms for the VSOB network based on the idea of inputs grouping. The two algorithms, namely plane fixed routing (PFR) algorithm and partially random routing (PRR) algorithm, have the time complexities of O(logN) and O( ) respectively, and FR algorithm can actually turn a VSOB network into a self-routing one. Extensive simulation based on a network simulator indicates that for large VSOB networks our new algorithms can achieve a reasonably low blocking probability while guarantee a very high switching speed. [ABSTRACT FROM AUTHOR]