Computational recognition of native-like folds of an anonymous amino acid sequence from a protein fold database is considered to be a promising approach to the three-dimensional (3D) fold prediction of the amino acid sequence. We present a new method for protein fold recognition through optimally aligning an amino acid sequence and a protein fold template (protein threading). The fitness of aligning an amino acid sequence with a fold template is measured by (1) the singleton fitness, representing the compatibility of substituting one amino acid by another and the combined preference of secondary structure and solvent accessibility for a particular amino acid, (2) the pairwise interaction, representing the contact preference between a pair of amino acids, and (3) alignment gap penalties. Though a protein threading problem so defined is known to be NP-hard in the most general sense, our algorithm runs efficiently if we place a cutoff distance on the pairwise interactions, as many of the existing threading programs do. For an amino acid sequence of size n and a fold template of size m with M core secondary structures, the algorithm finds an optimal alignment in O (Mn1.5C + 1 + mnC + 1) time and O (MnC + 1) space, where C is a (small) nonnegative integer, determined by a particular mathematical property of the pairwise interactions. As a case study, we have demonstrated that C is less than or equal to 4 for about 75% of the 293 unique folds in our protein database, when pairwise interactions are restricted to amino acids < or = 7 A apart (measured between their beta carbon atoms). An approximation scheme is developed for fold templates with C > 4, when threading requires too much memory and time to be practical on a typical workstation.