Computing the shortest path between a pair of vertices in a graph is a fundamental primitive in graph algorithmics. Classical exact methods for this problem do not scale up to contemporary, rapidly evolving social networks with hundreds of millions of users and billions of connections. A number of approximate methods have been proposed, including several landmark-based methods that have been shown to scale up to very large graphs with acceptable accuracy. This paper presents two improvements to existing landmarkbased shortest path estimation methods. The first improvement relates to the use of shortest-path trees (SPTs). Together with appropriate short-cutting heuristics, the use of SPTs allows to achieve higher accuracy with acceptable time and memory overhead. Furthermore, SPTs can be maintained incrementally under edge insertions and deletions, which allows for a fully-dynamic algorithm. The second improvement is a new landmark selection strategy that seeks to maximize the coverage of all shortest paths by the selected landmarks. The improved method is evaluated on the DBLP, Orkut, Twitter and Skype social networks.
New and compelling regulations (e.g., the GDPR in Europe) impose tremendous pressure on organizations, in order to adhere to standard procedures, processes, and practices. The field of conformance checking aims to quantify the extent to which the execution of a process, captured within recorded corresponding event data, conforms to a given reference process model. Existing techniques assume a post-mortem scenario, i.e. they detect deviations based on complete executions of the process. This limits their applicability in an online setting. In such context, we aim to to detect deviations online (i.e., in-vivo), in order to provide recovery possibilities before the execution of a process instance is completed. Also, current techniques assume cases to start from the initial stage of the process, whereas this assumption is not feasible in online settings. In this paper, we present a generic framework for online conformance checking, in which the underlying process is represented in terms of behavioural patterns and no assumption on the starting point of cases is needed. We instantiate the framework on the basis of Petri nets, with an accompanying new unfolding technique. The approach is implemented in the process mining tool ProM, and evaluated by means of several experiments including a stress-test and a comparison with a similar technique.
Automated process discovery techniques allow us to generate a process model from an event log consisting of a collection of business process execution traces. The quality of process models generated by these techniques can be assessed with respect to several criteria, including fitness, which captures the degree to which the generated process model is able to recognize the traces in the event log, and precision, which captures the extent to which the behavior allowed by the process model is observed in the event log. A range of fitness and precision measures have been proposed in the literature. However, recent studies have shown that these existing measures do not fulfil a set of intuitive properties, including monotonicity properties. In addition, existing fitness and precision measures suffer from scalability issues when applied to models discovered from real-life event logs. This article presents a family of fitness and precision measures based on the idea of comparing the k-th order Markovian abstraction of a process model against that of an event log. The article shows that this family of measures fulfils the aforementioned properties for suitably chosen values of k. An empirical evaluation shows that representative exemplars of this family of measures yield intuitive results on a synthetic dataset of model-log pairs, while outperforming existing measures of fitness and precision in terms of execution times on real-life event logs.
Automated process discovery techniques allow us to extract business process models from event logs. The quality of process models discovered by these techniques can be assessed with respect to various quality criteria related to simplicity and accuracy. One of these criteria, namely precision, captures the extent to which the behavior allowed by a discovered process model is observed in the log. While numerous measures of precision have been proposed in the literature, a recent study has shown that none of them fulfils a set of five axioms that capture intuitive properties behind the concept of precision. In addition, several existing precision measures suffer from scalability issues when applied to models discovered from real-life event logs. This paper presents a versatile framework for defining precision measures based on behavior abstractions. The key idea is that a precision measure can be defined by three ingredients: a function that abstracts a process model (e.g. as a transition system), a function that does the same for an event log, and a function that compares the behavior abstraction of the model with that of the log. We show empirically that different instances of this framework allow us to strike different tradeoffs between scalability and sensitivity. We also show that two instances of the framework based on lossless abstraction functions yield a precision measure that fulfils all the above-mentioned axioms. 1 A third accuracy criterion in automated process discovery is generalization: the extent to which the process model captures behavior that, while not observed in the log, is implied by it.
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