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A nonblocking photonic switch can be used to implement a tapped delay line with a large number of adaptive weights and a wide range of time delays. An advantage of using optical tapped delay lines for adaptive filtering is that the operating frequency can be quite high, in the 10-100 GHz range. We present a sparse reconfigurable adaptive filter (SRAF) based on a photonic switch with an input/output connection architecture that can be represented by a matrix of adaptive weights. This unique parallel structure can be reconfigured in an adaptive manner to implement a sparse filter impulse response for use in many applications. We consider an adaptive algorithm for this filter that chooses the input and output delays using a cross-correlation-based approach and connects these delays by weights that are adapted using a gradient algorithm. An alternative adaptive algorithm is also considered that is based on a system identification formulation where the weights are first adapted, and then the appropriate delay combinations are chosen. A search algorithm for implementing the connection constraint required by the SRAF is also discussed whereby each input is connected to only one output at any moment. Computer simulation examples are presented to illustrate the behavior of the filter for a system identification model.