On the graph traversal and linear binary-chain programs

Abstract

Grahne et al. have presented a graph algorithm for evaluating a subset of recursive queries [14], [15]. 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 Grahne's. The key idea of the improvement is to reduce the search space that will be traversed when a query is invoked. Furthermore, 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 acyclic and cyclic data.

Fast Algorithm for Calculating Transitive Closures of Binary Relations in the Structure of a Network Object

“…To solve these problems, many algorithms were developed and proposed at that time, which, in addition to constructing the TC itself, also optimize structures for representing and storing data in the memory of the computing system. These algorithms include algorithms that were presented in [11][12][13][14] and a number of others. A special attention deserves the work of H. Jagadish [15], in which the author proposed an indexing scheme that allows storing the computed TC in a compressed form, which makes it possible to reduce the size of the memory used.…”