Towards an Efficient SAT Encoding for Temporal Reasoning

In this paper, we investigate how an IA network can be effectively encoded into the SAT domain. We propose two basic approaches to modelling an IA network as a CSP: one represents the relations between intervals as variables and the other represents the relations between end-points of intervals as variables. By combining these two approaches with three different SAT encoding schemes, we produced six encoding schemes for converting IA to SAT. These encodings were empirically studied using randomly generated IA problems of sizes ranging from 20 to 100 nodes. A general conclusion we draw from these experimental results is that encoding IA into SAT produces better results than existing approaches. Further, we observe that the phase transition region maps directly from the IA encoding to each SAT encoding, but, surprisingly, the location of the hard region varies according to the encoding scheme. Our results also show a fixed performance ranking order over the various encoding schemes.