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Especially for verification purposes fingerprint§templates become ever more important. Thereto in§order to recognize a person a reference template must§be available, which can be stored for instance in a§database or on a RFID chip. With regard to mobile§storage media, and thus only a small amount of§memory, a need for compression arises. Such a§compression can be lossy, possible errors in the§recognition however, should be kept as small as§possible. In this book a new approach for the§compression of fingerprint templates is presented.§Such templates contain information about the§positions and orientations of the so-called minutiae,§which are in turn represented in the form of§d-dimensional points. So, the focus lies on the study§of graph-based approaches. The basic idea is to store§the difference vectors between always two points§instead of the minutiae. Since for this purpose§directed spanning trees allow an efficient encoding,§different approaches based on various spanning trees§are studied and evaluated.