Abstract The Nuclear Medicine Scheduling (NMS) problem consists of assigning patients to a day, on which the patient will undergo the medical check, the preparation and the actual image detection process. The schedule should consider the different requirements of the patients and the available resources, e.g. varying time required for different diseases and radiopharmaceuticals used, number of injection chairs and tomographs available. In this paper, we present two solutions to the NMS problem based on Answer Set Programming (ASP). The first solution is a direct ASP encoding, which is then processed by an ASP solver, while the second solution employs a Logic-based Bender Decomposition (LBBD) approach implemented through the usage of multi-shot solving. Experiments employing real data show that the direct encoding provides overall satisfying results in terms of solutions quality in a relatively short time, and that the LBBD approach also helps in improving scalability.

Abstract The Operating Room Scheduling (ORS) problem deals with the optimization of daily operating room surgery schedules. It is a challenging problem subject to many constraints, like to determine the starting time of different surgeries and allocating the required resources, including the availability of beds in different units. In the past years, Answer Set Programming (ASP) has been successfully employed for addressing and solving the ORS problem. Despite its importance, due to the inherent difficulty of retrieving real data, all the analyses on ORS ASP encodings have been performed on synthetic data so far. In this paper, first we present a new, improved ASP encoding for the ORS problem. Then, we deal with the real case of ASL1 Liguria, an Italian health authority operating through three hospitals, and present adaptations of the ASP encodings to deal with the real-world data. Further, we analyse the resulting encodings on hospital scheduling data by ASL1 Liguria. Results on some scenarios show that the ASP solutions produce satisfying schedules also when applied to such challenging, real data.1

Abstract Existential rules form an expressive ${{\textsf{Datalog}}}$ -based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass ${{\textsf{Datalog}}}$ and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $\mathcal{C}$ of existential rules, a new class called ${{\textsf{Dyadic-}\mathcal{C}}}$ enjoying the following properties: (i) it is decidable; (ii) it generalizes ${{\textsf{Datalog}}}$ ; (iii) it generalizes $\mathcal{C}$ ; (iv) it can effectively exploit any reasoner for query answering over $\mathcal{C}$ ; and (v) its computational complexity does not exceed the highest between the one of $\mathcal{C}$ and the one of ${{\textsf{Datalog}}}$ .