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.

Constraint Programming has proven to be an effective platform for constraint based sequence mining. Previous work has focussed on standard frequent sequence mining, as well as frequent sequence mining with a maximum 'gap' between two matching events in a sequence. The main challenge in the latter is that this constraint can not be imposed independently of the omnipresent frequency constraint. Indeed, the gap constraint changes when a subsequence is included in a sequence. In this work, we go beyond that and investigate the integration of timed events, the gap constraint as well as the span constraint that constrains the time between the first and last matching event. We show how the three are interrelated, and what the required changes to the frequency constraint are. Key in our approach is the concept of an extension window defined by gap/span and we develop techniques to avoid scanning the sequences needlessly, as well as using a backtracking-aware datastructure. Experiments demonstrate that the proposed approach outperforms both specialized and CP-based approaches in most cases and that the difference becomes increasingly large for low frequency thresholds.

1 UCLouvain, ICTEAM (Belgium); 2 UAC, ED-SDI (Benin)3 VUB Brussels (Belgium) and KU Leuven (Belgium) {john.aoga,pierre.schaus}@uclouvain.be; tias.guns@{vub.be,cs.kuleuven.be} Abstract. Constraint Programming is becoming competitive for solving certain data-mining problems largely due to the development of global constraints. We introduce the CoverSize constraint for itemset mining problems, a global constraint for counting and constraining the number of transactions covered by the itemset decision variables. We show the relation of this constraint to the well-known table constraint, and our filtering algorithm internally uses the reversible sparse bitset data structure recently proposed for filtering table. Furthermore, we expose the size of the cover as a variable, which opens up new modelling perspectives compared to an existing global constraint for (closed) frequent itemset mining. For example, one can constrain minimum frequency or compare the frequency of an itemset in different datasets as is done in discriminative itemset mining. We demonstrate experimentally on the frequent, closed and discriminative itemset mining problems that the CoverSize constraint with reversible sparse bitsets allows to outperform other CP approaches.