Ordering Depth First Search to Improve AFD Mining

This paper describes a new search algorithm, bottom-up attribute keyness depth-first search (BU-AKD), for mining powerset lattices with the use of a monotonic approximation measure; characteristics present in many problem domains. The research reported here focuses on one of these problem domains, the discovery of Approximate Functional Dependencies (AFDs). AFDs are measured versions of functional dependencies, which have received attention from the relational database and machine learning communities. Bottomup depth-first search, BU-DFS, algorithms in general can improve efficiency over the traditional bottom-up breadth first search algorithm by doing a better job of avoiding the calculation of the approximation measure based on information learned as the search space is explored. The goal of BU-AKD is to resolve one important drawback of BU-DFS algorithms which makes their use in practice problematic their inconsistent runtime performance as search parameters vary. The approach that BU-AKD takes is to use a heuristic to guide the exploration of a lattice which adapts to the search parameters, thus, providing consistent performance comparable to best-performing BU-DFS algorithms. This paper reports a variety of experiments which evaluate BUAKD and other algorithms using an algorithmic, machineindependent cost measure, as well as traditional runtime tests. Experimental results show that BU-AKD performs consistently well and validates a number of insights used in its design.