Geometry-based propagation of temporal constraints

In recent years, the Internet of Things (IoT) has been introduced to offer promising solutions in many areas. A big challenge faced by the IoT is to integrate heterogeneous information sources and process information effectively. As an important element in information integration, temporal reasoning is highly related to the dynamic, sequential aspect of both the information integration and the decision making process. Focusing on temporal reasoning, this paper introduces a method to represent both qualitative and quantitative temporal constraints in a 2-dimensional (2-D) space. Meanwhile, an efficient constraint-based geometric (CG) algorithm for propagating constraints (including inherent constraints and constraint pairs) on events in a 2-D space is proposed. A geometric recombination and intersection (GRI) method, a part of the CG algorithm, is presented to propagate one constraint pair from a geometric point. The experimental results show that in terms of both constructed and realistic benchmarks, the CG algorithm outperforms the existing Floyd-Warshall’s algorithm with the time complexity of O(n³), especially for benchmarks with a large number of events.