## 2 New Frontiers
In particular, SAT solvers are often used in practice, and are very effective for this purpose. Set in the framework of Parameterized Complexity, this can mean that the objective is to design FPT-time reductions in SAT. Of course, this makes sense only for problems that are supposed not to be NP-complete, but belong to higher levels of the Polynomial Hierarchy. In this way, we harness the power of both Parameterized Complexity and SAT solvers, aiming to develop practical algorithms for very hard problems. In this collection, a comprehensive compendium by [PERSON] and [PERSON] discusses this framework and presents a long list of relevant problems that are known to be reducible in FPT time to SAT. The \"Best\" Solution and the \"Correct\" Input.Motivated by both theoretical and practical considerations, the study of enumeration and counting problems is of broad interest. Indeed, in many scenarios that arise in practice, we might not be interested in computing a single solution, but we may be interested in several--and possibly even all--solutions to a given problem, or just to count how many solutions there are. For example, in many problems that arise in bioinformatics, it is not clear what the \"best\" solution is, since different solutions can represent different biological explanations (e.g., describe different evolutionary events), and it is not clear which is the correct one. In some cases, but not all, after offering these solutions, further experiments can be used to further sieve them. Therefore, perhaps the \(t\) \"best\" (or some \(t\)) solutions are sought. This yields different questions in enumeration, where we wish to list all solutions, some \(t\) best solutions, or each of the solutions one by one with modest delay. Clearly, the last option is the least restrictive if we enumerate the solution from \"best\" to \"worse\". The study of enumeration in the framework of Parameterized Complexity is relatively young. Here, when interested in the last option, we want the delay time to be FPT. Problems that admit enumeration algorithm with an FPT delay time are said to belong to the class DelayFPT. [PERSON] et al. study this setting, and present corresponding algorithms for modification problems on graphs and beyond. When seeking some collection, say, of size \(t\), of solutions, we may wish them to be \"diverse\", in some sense. Indeed, we may not have a reliable measure for what the \(t\) \"best\" solutions are, or perhaps we want to represent the entire solution space. In both cases, we may want the \(t\) output solutions to be, in some sense, as \"diverse\" as possible. There are various measures for the diversity of a collection. In particular, the work of [PERSON] et al. makes use of the sum of the \"distances\" between every pair of output solutions. Specifically, they present parameterized algorithms to output a collection of \(t\) solutions for the \(d\)-Hitting Set problem (which are hitting sets whose size is, at most, some input parameter \(k\)), whose diversity measure is, at least, some input parameter \(p\), where the distance between two solutions is the size of their symmetric difference. Besides being uncertain about which solution we seek, we might be uncertain about the input itself. In particular, for a graph problem, we might be uncertain about which edges should exist--for example, in protein-protein-interaction networks, where vertices represent proteins and edges represent interactions between them, noisy and error-prone experiments to determine the interactions lead to uncertainty. [PERSON] and [PERSON] survey different models of uncertainty as well as problems corresponding to them, some of which are motivated by biological and social networks. In addition, they zoom into the problem of finding the maximal core of a graph under uncertainty in two models, and present polynomial-time and FPT algorithms as well as a W[1]-hardness result.