Abel Armas-Cervantes

Fast fully dynamic landmark-based estimation of shortest path distances in very large graphs

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 landmark-based 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.

Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures

We address the problem of diagnosing behavioral differences between pairs of business process models. Specifically, given two process models, we seek to determine if they are behaviorally equivalent, and if not, we seek to describe their differences in terms of behavioral relations captured in one model but not in the other. The proposed solution is based on a translation from process models to Asymmetric Event Structures (AES). A naive version of this translation suffers from two limitations. First, it produces redundant difference diagnostic statements because an AES may contain unnecessary event duplication. Second, it is not applicable to process models with cycles. To tackle the first limitation, we propose a technique to reduce event duplication in an AES while preserving canonicity. For the second limitation, we propose a notion of unfolding that captures all possible causes of each event in a cycle. From there we derive an AES where repeated events are distinguished from non-repeated ones and that allows us to diagnose differences in terms of repetition and causal relations in one model but not in the other.

Diagnosing behavioral differences between business process models

Companies operating in multiple markets or segments often need to manage multiple variants of the same business process. Such multiplicity may stem for example from distinct products, different types of customers or regulatory differences across countries in which the companies operate. During the management of these processes, analysts need to compare models of multiple process variants in order to identify opportunities for standardization or to understand performance differences across variants. To support this comparison, this paper proposes a technique for diagnosing behavioral differences between process models. Given two process models, it determines if they are behaviorally equivalent, and if not, it describes their differences in terms of behavioral relations - like causal dependencies or conflicts - that hold in one model but not in the other. The technique is based on a translation from process models to event structures, a formalism that describes the behavior as a collection of events (task instances) connected by binary behavioral relations. A naive version of this translation suffers from two limitations. First, it produces redundant difference statements because an event structure describing a process may contain unnecessary event duplications. Second, this translation is not directly applicable to process models with cycles as the corresponding event structure is infinite. To tackle the first issue, the paper proposes a technique for reducing the number of events in an event structure while preserving the behavior. For the second issue, relying on the theory of complete unfolding prefixes, the paper shows how to construct a finite prefix of the unfolding of a possibly cyclic process model where all possible causes of every activity is represented. Additionally, activities that can occur multiple times in an execution of the process are distinguished from those that can occur at most once. The finite prefix thus enables the diagnosis of behavioral differences in terms of activity repetition and causal relations that hold in one model but not in the other. The method is implemented as a prototype that takes as input process models in the Business Process Model and Notation (BPMN) and produces difference statements in natural language. Differences can also be graphically overlaid on the process models.

On the expressive power of behavioral profiles

Behavioral profiles have been proposed as a behavioral abstraction of dynamic systems, specifically in the context of business process modeling. A behavioral profile can be seen as a complete graph over a set of task labels, where each edge is annotated with one relation from a given set of binary behavioral relations. Since their introduction, behavioral profiles were argued to provide a convenient way for comparing pairs of process models with respect to their behavior or computing behavioral similarity between process models. Still, as of today, there is little understanding of the expressive power of behavioral profiles. Via counter-examples, several authors have shown that behavioral profiles over various sets of behavioral relations cannot distinguish certain systems up to trace equivalence, even for restricted classes of systems represented as safe workflow nets. This paper studies the expressive power of behavioral profiles from two angles. Firstly, the paper investigates the expressive power of behavioral profiles and systems captured as acyclic workflow nets. It is shown that for unlabeled acyclic workflow net systems, behavioral profiles over a simple set of behavioral relations are expressive up to configuration equivalence. When systems are labeled, this result does not hold for any of several previously proposed sets of behavioral relations. Secondly, the paper compares the expressive power of behavioral profiles and regular languages. It is shown that for any set of behavioral relations, behavioral profiles are strictly less expressive than regular languages, entailing that behavioral profiles cannot be used to decide trace equivalence of finite automata and thus Petri nets.

Reduction of event structures under history preserving bisimulation

Abstract Event structures represent concurrent processes in terms of events and dependency relations between events like causality and conflict. Since the introduction of prime event structures, many variants of event structures have been proposed with different dependency relations and, hence, with differences in their expressive power. One of the possible benefits of using a more expressive event structure model is that of obtaining a more compact representation for the same behaviour using a smaller number of events. This article addresses the problem of reducing the size of an event structure while preserving its behaviour under a classical notion of behavioural equivalence in the true concurrency spectrum, namely history preserving bisimulation. In particular, we investigate this problem on two generalisations of prime event structures: asymmetric event structures, which rely on an asymmetric form of conflict, and flow event structures, which support a form of disjunctive causality. We single out conditions under which distinct events in an event structure can be seen as occurrences of the same activity in different contexts and thus can be folded into a single event without altering the original behaviour. By iterating the folding operation, any finite event structure can be reduced to a minimal form, behaviourally equivalent to the original one. This is not unique in general, as it depends on the order on which the folding operations are applied.

Scalable Conformance Checking of Business Processes

Given a process model representing the expected behavior of a business process and an event log recording its actual execution, the problem of business process conformance checking is that of detecting and describing the differences between the process model and the log. A desirable feature is to produce a minimal yet complete set of behavioral differences. Existing conformance checking techniques that achieve these properties do not scale up to real-life process models and logs. This paper presents an approach that addresses this shortcoming by exploiting automata-based techniques. A log is converted into a deterministic automaton in a lossless manner, the input process model is converted into another minimal automaton, and a minimal error-correcting synchronized product of both automata is calculated using an A* heuristic. The resulting automaton is used to extract alignments between traces of the model and traces of the log, or statements describing behavior observed in the log but not captured in the model. An evaluation on synthetic and real-life models and logs shows that the proposed approach outperforms a state-of-the-art method for complete conformance checking.

Event Structures as a Foundation for Process Model Differencing, Part 1: Acyclic processes

This paper considers the problem of comparing process models in terms of their behavior. Given two process models, the problem addressed is that of explaining their differences in terms of simple and intuitive statements. This model differencing operation is needed for example in the context of process consolidation, where analysts need to reconcile differences between process variants in order to produce consolidated process models. The paper presents an approach to acyclic process model differencing based on event structures. First the paper considers the use of prime event structures. It is found that the high level of node duplication inherent to prime event structures hinders on the usefulness of the difference diagnostics that can be extracted thereon. Accordingly, the paper defines a method for producing (asymmetric) event structures with reduced duplication.

On the Suitability of Generalized Behavioral Profiles for Process Model Comparison

Given two process models, the problem of behavioral comparison is that of determining if these models are behaviorally equivalent (e.g., by trace equivalence) and, if not, identifying how can the differences be presented in a compact manner? Behavioral profiles have been proposed as a convenient abstraction for this problem. A behavioral profile is a matrix, where each cell encodes a behavioral relation between a pair of tasks (e.g., causality or conflict). Thus, the problem of behavioral comparison can be reduced to matrix comparison. It has been observed that while behavioral profiles can be efficiently computed, they are not accurate insofar as behaviorally different process models may map to the same behavioral profile. This paper investigates the question of how accurate existing behavioral profiles are. The paper shows that behavioral profiles are fully behavior preserving for the class of acyclic unlabeled nets with respect to configuration equivalence. However, for the general class of acyclic nets, existing behavioral profiles are exponentially inaccurate, meaning that two acyclic nets with the same behavioral profile may differ in an exponential number of configurations.

Online Conformance Checking Using Behavioural Patterns

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 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.