Temporal Graph Functional Dependencies: Technical Report
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Data dependencies have been extended to graphs e.g., graph functional dependencies (GFDs) to characterize the topological and value constraints in graphs. Existing graph dependencies are defined for static graphs. Nevertheless, temporal data constraints may hold over evolving graphs for certain periods. The need for characterizing temporal graph dependencies is evident in anomaly detection and predictive analysis for dynamic networks. This paper studies a new class of graph dependencies called Temporal Graph Functional Dependencies (TGFDs). TGFDs generalize conventional functional dependencies to a collection of graph snapshots induced by time intervals, and enforce both topological constraints and attribute value dependencies that must be satisfied by these snapshots. (1) We establish the complexity results for satisfiability and implication of TGFDs, and verify that these problems do not become harder than their GFDs counterparts. (2) We propose a sound and complete axiomatization system for TGFDs. (3) We also present an efficient parallel algorithm to detect violations of TGFDs. The algorithm exploits data locality induced by temporal constraints, incremental pattern matching, and load balancing strategies for feasible error detection in large temporal graphs. Our evaluation over real datasets show that our algorithms achieve 29 runtimes, and up to +55
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