In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[Q]: The weighted Maximum Satisfiability problem (weighted MAX-SAT) is a NP-hard problem with numerous applications arising in artificial intelligence. As an efficient tool for heuristic design, the backbone has been applied to heuristics design for many NP-hard problems. In this paper, we investigated the computational complexity for retrieving the backbone in weighted MAX-SAT and developed a new algorithm for solving this problem. We showed that it is intractable to retrieve the full backbone under the assumption that NP P  . Moreover, it is intractable to retrieve a fixed fraction of the backbone as well. And then we presented a backbone guided local search (BGLS) with Walksat operator for weighted MAX-SAT. BGLS consists of two phases: the first phase samples the backbone information from local optima and the backbone phase conducts local search under the guideline of backbone. Extensive experimental results on the benchmark showed that BGLS outperforms the existing heuristics in both solution quality and runtime.
[A]: Approximating the Backbone in the Weighted Maximum Satisfiability Problem


[Q]: We introduce a simple, general framework for likelihood-free Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The advantage is that we only require a prior distribution on a class of simulators. This is useful when a probabilistic model of the underlying process is too complex to formulate, but where detailed simulation models are available. ABC-RL allows the use of any Bayesian reinforcement learning technique in this case. It can be seen as an extension of simulation methods to both planning and inference. We experimentally demonstrate the potential of this approach in a comparison with LSPI. Finally, we introduce a theorem showing that ABC is sound.
[A]: ABC Reinforcement Learning


[Q]: The main advantage of Constraint Programming (CP) approaches for sequential pattern mining (SPM) is their modularity, which includes the ability to add new constraints (regular expressions, length restrictions, etc). The current best CP approach for SPM uses a global constraint (module) that computes the projected database and enforces the minimum frequency; it does this with a filtering algorithm similar to the PrefixSpan method. However, the resulting system is not as scalable as some of the most advanced mining systems like Zaki’s cSPADE. We show how, using techniques from both data mining and CP, one can use a generic constraint solver and yet outperform existing specialized systems. This is mainly due to two improvements in the module that computes the projected frequencies: first, computing the projected database can be sped up by pre-computing the positions at which an symbol can become unsupported by a sequence, thereby avoiding to scan the full sequence each time; and second by taking inspiration from the trailing used in CP solvers to devise a backtracking-aware data structure that allows fast incremental storing and restoring of the projected database. Detailed experiments show how this approach outperforms existing CP as well as specialized systems for SPM, and that the gain in efficiency translates directly into increased efficiency for other settings such as mining with regular expressions.
[A]:
An Efficient Algorithm for Mining Frequent Sequence with Constraint Programming