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All-optical multifiber networks may require large and expensive optical switches (i.e., optical switches with many inputs/outputs). To tackle this problem, the existing approach adopts an individual node perspective and focuses on designing the internal node architectures that require smaller optical switches (i.e., optical switches with fewer inputs/outputs). In this paper, we adopt an entire network perspective and propose a logical subnetting approach to further reduce the switch size required. We use multiple logical subnets to compose a network, where a subnet has the same physical topology as but smaller dimensions than the network. In each subnet, each node has fewer incoming/outgoing fibers and hence it requires smaller optical switches. A lightpath can be set up through any one of the available subnets. We propose two subnetting methods: (i) homogeneous subnetting in which all subnets are identical and (ii) heterogeneous subnetting in which different subnets may adopt different node architectures and dimensions. Logical subnetting has three advantages: (i) the resulting network requires significantly smaller optical switches, while its blocking probability can be nearly the same, (ii) logical subnetting can complement any existing node architectures to integrate their respective advantages and further reduce the switch size required, and (iii) an existing network can easily be scaled up by adding additional subnets without modifying the existing ones.