We study the problem of listing all closed sets of a closure operator a that is a partial function on the power set of some finite ground set E, i.e., sigma : F -> F with F subset of P(E). A very simple divide-and-conquer algorithm is analyzed that correctly solves this problem if and only if the domain of the closure operator is a strongly accessible set system. Strong accessibility is a strict relaxation of greedoids as well as of independence systems. This algorithm turns out to have delay O (vertical bar E vertical bar (T-F + T-sigma + vertical bar E vertical bar)) and space O (vertical bar E vertical bar + S-F + S-sigma), where T-F, S-F, T-sigma, and S-sigma are the time and space complexities of checking membership in F and computing a, respectively. In contrast, we show that the problem becomes intractable for accessible set systems. We relate our results to the data mining problem of listing all support-closed patterns of a dataset and show that there is a corresponding closure operator for all datasets if and only if the set system satisfies a certain confluence property

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BackgroundMaking forecasts about biodiversity and giving support to policy relies increasingly on large collections of data held electronically, and on substantial computational capability and capacity to analyse, model, simulate and predict using such data. However, the physically distributed nature of data resources and of expertise in advanced analytical tools creates many challenges for the modern scientist. Across the wider biological sciences, presenting such capabilities on the Internet (as “Web services”) and using scientific workflow systems to compose them for particular tasks is a practical way to carry out robust “in silico” science. However, use of this approach in biodiversity science and ecology has thus far been quite limited.ResultsBioVeL is a virtual laboratory for data analysis and modelling in biodiversity science and ecology, freely accessible via the Internet. BioVeL includes functions for accessing and analysing data through curated Web services; for performing complex in silico analysis through exposure of R programs, workflows, and batch processing functions; for on-line collaboration through sharing of workflows and workflow runs; for experiment documentation through reproducibility and repeatability; and for computational support via seamless connections to supporting computing infrastructures. We developed and improved more than 60 Web services with significant potential in many different kinds of data analysis and modelling tasks. We composed reusable workflows using these Web services, also incorporating R programs. Deploying these tools into an easy-to-use and accessible ‘virtual laboratory’, free via the Internet, we applied the workflows in several diverse case studies. We opened the virtual laboratory for public use and through a programme of external engagement we actively encouraged scientists and third party application and tool developers to try out the services and contribute to the activity.ConclusionsOur work shows we can deliver an operational, scalable and flexible Internet-based virtual laboratory to meet new demands for data processing and analysis in biodiversity science and ecology. In particular, we have successfully integrated existing and popular tools and practices from different scientific disciplines to be used in biodiversity and ecological research.Electronic supplementary materialThe online version of this article (doi:10.1186/s12898-016-0103-y) contains supplementary material, which is available to authorized users.

Abstract. Many problems in data mining can be viewed as a special case of the problem of enumerating the closed elements of an independence system with respect to some specific closure operator. Motivated by real-world applications, e.g., in track mining, we consider a generalization of this problem to strongly accessible set systems and arbitrary closure operators. For this more general problem setting, the closed sets can be enumerated with polynomial delay if deciding membership in the set system and computing the closure operator can be solved in polynomial time. We discuss potential applications in graph mining.

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