Abstract
In this paper we present a novel pseudo-Boolean (PB) constraint encoding for solving the weighted MaxSAT problem with iterative SAT-based methods based on the Polynomial Watchdog (PW) CNF encoding. The watchdog of the PW encoding indicates whether the bound of the PB constraint holds. In our approach, we lift this static watchdog concept to a dynamic one allowing an incremental convergence to the optimal result. Consequently, we formulate and implement a SAT-based algorithm for our new Dynamic Polynomial Watchdog (DPW) encoding which can be applied for solving the MaxSAT problem. Furthermore, we introduce three fundamental optimizations of the PW encoding also suited for the original version leading to significantly less encoding size. Our experimental results show that our encoding and algorithm is competitive with state-of-the-art encodings as utilized in QMaxSAT (2nd place in last MaxSAT Evaluation 2017). Our encoding dominates two of the QMaxSAT encodings, and at the same time is able to solve unique instances. We integrated our new encoding into QMaxSAT and adapt the heuristic to choose between the only remaining encoding of QMaxSAT and our approach. This combined version solves 19 (4%) more instances in overall 30% less run time on the benchmark set of the MaxSAT Evaluation 2017. Compared to each encoding of QMaxSAT used in the evaluation, our encoding leads to an algorithm that is on average at least 2X faster.
This work is partially supported by the DFG project “Algebraic Fault Attacks” (funding id PO 1220/7-1, BE 1176 20/1, KR 1907/6-1).
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Notes
- 1.
Note that tare values of zero do not have any influence. Hence, only the tare bits \(T_i=1\) are added to \(TB_i\), and are also directly set to 1.
- 2.
The run time difference to Table 1 is caused by the time needed for the encoding and the remaining part of our algorithm (e.g. analyzing the SAT solver model).
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Paxian, T., Reimer, S., Becker, B. (2018). Dynamic Polynomial Watchdog Encoding for Solving Weighted MaxSAT. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_3
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