Sequential Pattern Mining (SPM) is a prominent topic in unsupervised learning that aims at finding frequent patterns of events in sequential datasets. Frequent patterns have a wide range of applications and are used, for example, to develop novel association rules, aid supervised learners in prediction tasks, and design effective recommender systems. While supervised learning algorithms have enjoyed great success in using large-size datasets for better prediction accuracy, unsupervised algorithms such as SPM are still faced with challenges in scalability and memory requirement. In particular, the two dominant SPM methodologies, Apriori (Agrawal et al., 1994) and prefix-projection (Han et al., 2001), suffer from the explosion of candidate patterns or require to fit in memory the entire large-size training dataset. This memory bottleneck is aggravated by the steady increase of dataset size in recent years, which may contain a larger and richer set of frequent patterns to be investigated. It is thus vital for the success of SPM algorithms that they adapt to their rapidly growing data environment. This paper investigates the role of dataset models in the time and memory efficiency of SPM algorithms.

Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.

Compilation techniques in planning reformulate a problem into an alternative encoding for which efficient, off-the-shelf solvers are available. In this work, we present a novel mixed-integer linear programming (MILP) compilation for cost-optimal numeric planning with instantaneous actions. While recent works on the problem are restricted to actions that modify variables present in simple numeric conditions, our MILP formulation, in addition, handles linear conditions and linear action effects on numeric state variables. Such problems are particularly challenging due to the state-dependency of the action effects. Experiments show that our approach, in addition to being the state of the art for the more general problem class, is competitive with heuristic search-based planners on domains with only simple numeric conditions.

Linear programming has been successfully used to compute admissible heuristics for cost-optimal classical planning. Although one of the strengths of linear programming is the ability to express and reason about numeric variables and constraints, their use in numeric planning is limited. In this work, we extend linear programming-based heuristics for classical planning to support numeric state variables. In particular, we propose a model for the interval relaxation, coupled with landmarks and state equation constraints. We consider both linear programming models and their harder-to-solve, yet more informative, integer programming versions. Our experimental analysis shows that considering an NP-Hard heuristic often pays off and that A* search using our integer programming heuristics establishes a new state of the art in cost-optimal numeric planning.