Networks of workstations are rapidly emerging as a cost-effective alternative to parallel computers. Switch-based interconnects with irregular topology allow the wiring flexibility, scalability, and incremental expansion capability required in this environment. However, the irregularity also makes routing and deadlock avoidance on such systems quite complicated. In current proposals, many messages are routed following nonminimal paths, increasing latency and wasting resources. In this paper, we propose two general methodologies for the design of adaptive routing algorithms for networks with irregular topology. Routing algorithms designed according to these methodologies allow messages to follow minimal paths in most cases, reducing message latency and increasing network throughput. As an example of application, we propose two adaptive routing algorithms for ANI (previously known as Autonet). They can be implemented either by duplicating physical channels or by splitting each physical channel into two virtual channels. In the former case, the implementation does not require a new switch design. It only requires changing the routing tables and adding links in parallel with existing ones, taking advantage of spare switch ports. In the latter case, a new switch design is required, but the network topology is not changed. Evaluation results for several different tapologies and message distributions show that the new routing algorithms are able to increase throughput for random traffic by a factor of up to 4 with respect to the original up*/down* algorithm, also reducing latency significantly. For other message distributions, throughput is increased more than seven times. We also show that most of the improvement comes from the use of minimal routing.