Supplementary Data : ACM - BCB 2010

Shortest transitive edge relation presents an alternative to transitive closure relation for answering a class of complex biological queries that requires connectivity information but not the full transitive closure. A biological querie such “ find each downstream protein interacting with glutamine synthetase using five or fewer interactions ” does not require transitive closure. Shortest transitive edge relation is an alternative to transitive closure that does not suffer from some of the drawbacks of using transitive closure such as increased space complexity with increased distance. Instead of computing each transitive edge between two nodes as is the case with transitive closure only the shortest distance transitive edges are computed. We present a join algorithm, MinJoinLogarithmicTC, for computing shortest transitive edge relation. MinJoinLogarithmicTC takes advantage of domain requirements (need to only compute shortest distance transitive edge) to more efficiently compute shortest transitive edge relation. It achieves this efficiency by avoiding join operations that would lead to transitive edges with distances greater than the shortest distance. In query optimization, selection of rows is sometimes done as early as possible, especially when join operations are involved. The rationale behind this rule is that a join operation can operate on a smaller table reducing work [2]. Using the same principle MinJoinLogarithmicTC eliminates rows from input relations to join operations that would lead to transitive edges with distances greater than the shortest distance transitive edge. The smaller input relations will lead to reduced join operations and better performance. Before presenting the details of MinJoinLogarithmicTC, we will present LogarithmicTC. LogarithmicTC is a modified version of an algorithm previously discussed by Valduriez and Boral [4]. In Section 2, MinJoinLogarithmicTC is compared with LogarithmicTC to demonstrate its efficiency in computing shortest distance transitive edge relation.