Constraint Programming for Mining Borders of Frequent Itemsets

Frequent itemset mining is one of the most studied tasks in knowledge discovery. It is often reduced to mining the positive border of frequent itemsets, i.e. maximal frequent itemsets. Infrequent itemset mining, on the other hand, can be reduced to mining the negative border, i.e. minimal infrequent itemsets. We propose a generic framework based on constraint programming to mine both borders of frequent itemsets.One can easily decide which border to mine by setting a simple parameter. For this, we introduce two new global constraints, FREQUENTSUBS and INFREQUENTSUPERS, with complete polynomial propagators. We then consider the problem of mining borders with additional constraints. We prove that this problem is coNP-hard, ruling out the hope for the existence of a single CSP solving this problem (unless coNP ⊆ NP).

Clingcon: The next generation

We present the third generation of the constraint answer set systemclingcon, combining Answer Set Programming (ASP) with finite domain constraint processing (CP). While its predecessors rely on a black-box approach to hybrid solving by integrating the CP solvergecode, the newclingconsystem pursues a lazy approach using dedicated constraint propagators to extend propagation in the underlying ASP solverclasp. No extension is needed for parsing and groundingclingcon's hybrid modeling language since both can be accommodated by the new generic theory handling capabilities of the ASP groundergringo. As a whole,clingcon3 is thus an extension of the ASP systemclingo5, which itself relies on the groundergringoand the solverclasp. The new approach ofclingconoffers a seamless integration of CP propagation into ASP solving that benefits from the whole spectrum ofclasp's reasoning modes, including, for instance, multi-shot solving and advanced optimization techniques. This is accomplished by a lazy approach that unfolds the representation of constraints and adds it to that of the logic program only when needed. Although the unfolding is usually dictated by the constraint propagators during solving, it can already be partially (or even totally) done during preprocessing. Moreover,clingcon's constraint preprocessing and propagation incorporate several well-established CP techniques that greatly improve its performance. We demonstrate this via an extensive empirical evaluation contrasting, first, the various techniques in the context of CSP solving and, second, the newclingconsystem with other hybrid ASP systems.

T-SATPLAN: A SAT-BASED TEMPORAL PLANNER

Recent advances in solving constraint satisfaction problems (CSPs) and heuristic search have made it possible to solve classical planning problems significantly faster. There is an increasing amount of work on extending these advances to solving planning problems in more expressive languages. These problems and languages contain metric time, quantifiers and resource quantities. SAT-based approaches are very effective at optimal planning. In this paper we report on SAT-based temporal planner T-SATPLAN. One key challenge in the development of planners casting planning as SAT or CSP is the identification of constraints which are satisfied if and only if there is a plan of k steps. In this paper we show how such a SAT encoding can be synthesized for temporal planning. As part of this, we generalize explanatory frame axioms for two states of fluents (true, false) to three states of fluents (true, false and undefined). We show how this SAT encoding can be simplified. We discuss two additional SAT encodings of temporal planning. The encoding schemes make it easier to exploit progress in SAT and CSP solving to solve temporal planning problems. We also report on an experimental evaluation of T-SATPLAN using one such encoding scheme. The evaluation shows that significantly large SAT encodings of temporal planning problems can be solved extremely fast.