An optimal graph traversal algorithm for evaluating linear binary-chain programs

TL;DR: A new algorithm is described which requires less time than the algorithm of Grahne et al. and achieves a linear time complexity for both cyclic and non-cyclic data.

Abstract: Grahne et al. have presented a graph algorithm for a subset of recursive queries. This method consists of two phases. In the first phase, the method transforms a linear binary-chain program into a set of equations over expressions containing predicate symbols. In the second phase, a graph is constructed from the equations and the answers are produced by traversing the relevant paths. Here we describe a new algorithm which requires less time than the algorithm of Grahne et al. The key idea of the improvement is to reduce the search space that will be traversed when a query is invoked. Further, we speed up the evaluation of cyclic data by generating most answers directly in terms of the answers already found and the associated “path information” instead of traversing the corresponding paths as usual. In this way, our algorithm achieves a linear time complexity for both cyclic and non-cyclic data.