We describe a method, “Shortest Path Segmentation” (SPS), which combines dynamic programming and a neural net recognizer for segmenting and recognizing character strings. We describe the application of this method to two problems: recognition of handwritten ZIP Codes, and recognition of handwritten words. For the ZIP Codes, we also used the method to automatically segment the images during training: the dynamic programming stage both performs the segmentation and provides inputs and desired outputs to the neural network. Results are reported for a test set of 2642 unsegmented handwritten 212 dpi binary ZIP Code (5- and 9-digit) images. For handwritten word recognition, we combined SPS with a “Space Displacement Neural Network” approach, in which a single-character-recognition network is extended over the entire word image, and in which SPS techniques are then used to rank order a given lexicon. We report results on a test set of 3000 300 ppi gray scale word images, extracted from images of live mail pieces, for lexicons of size 10, 100, and 1000. Representing the problem as a graph as proposed in this paper has advantages beyond the efficient finding of the final optimal segmentation, or the automatic segmentation of images during training. We can also easily extend the technique to generate K “runner up” answers (for example, by finding the K shortest paths). This paper will also describe applications of some of these ideas.