Antibodies that bind to protein surfaces of interest can be used to report the three-dimensional structure of the protein as follows: Proteins are composed of linear polypeptide chains that fold together in complex spatial patterns to create the native protein structure. These folded structures form binding sites for antibodies. Antibody binding sites are typically "assembled" on the protein surface from segments that are far apart in the primary amino acid sequence of the target proteins. Short amino acid probe sequences that bind to the active region of each antibody can be used as witnesses to the antibody epitope surface and these probes can be efficiently selected from random sequence peptide libraries. This paper presents a new method to align these antibody epitopes to discontinuous regions of the one-dimensional amino acid sequence of a target protein. Such alignments of the epitopes indicate how segments of the protein sequence must be folded together in space and thus provide long-range constraints for solving the 3-D protein structure. This new antibody-based approach is applicable to the large fraction of proteins that are refractory to current approaches for structure determination and has the additional advantage of requiring very small amounts of the target protein. The binding site of an antibody is a surface, not just a continuous linear sequence, so the epitope mapping alignment problem is outside the scope of classical string alignment algorithms, such as Smith-Waterman. We formalize the alignment problem that is at the heart of this new approach, prove that the epitope mapping alignment problem is NP-complete, and give some initial results using a branch-and-bound algorithm to map two real-life cases. Initial results for two validation cases are presented for a graph-based protein surface neighbor mapping procedure that promises to provide additional spatial proximity information for the amino acid residues on the protein surface.