We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient at first glance, the key ingredient introduced here is pruning during breadth-first searches. While we can still answer the correct distance for any pair of vertices from the labels, it surprisingly reduces the search space and sizes of labels. Moreover, we show that we can perform 32 or 64 breadth-first searches simultaneously exploiting bitwise operations. We experimentally demonstrate that the combination of these two techniques is efficient and robust on various kinds of large-scale real-world networks. In particular, our method can handle social networks and web graphs with hundreds of millions of edges, which are two orders of magnitude larger than the limits of previous exact methods, with comparable query time to those of previous methods.

Fast Exact Shortest-Path Distance Queries on Large Networks by Pruned Landmark Labeling

Fast exact shortest-path distance queries on large networks by pruned landmark labeling

We consider the point-to-point (approximate) shortest-path query problem, which is the following generalization of the classical single-source (SSSP) and all-pairs shortest-path (APSP) problems: we are first presented with a network (graph). A so-called preprocessing algorithm may compute certain information (a data structure or index) to prepare for the next phase. After this preprocessing step, applications may ask shortest-path or distance queries, which should be answered as fast as possible.Due to its many applications in areas such as transportation, networking, and social science, this problem has been considered by researchers from various communities (sometimes under different names): algorithm engineers construct fast route planning methods; database and information systems researchers investigate materialization tradeoffs, query processing on spatial networks, and reachability queries; and theoretical computer scientists analyze distance oracles and sparse spanners. Related problems are considered for compact routing and distance labeling schemes in networking and distributed computing and for metric embeddings in geometry as well.In this survey, we review selected approaches, algorithms, and results on shortest-path queries from these fields, with the main focus lying on the tradeoff between the index size and the query time. We survey methods for general graphs as well as specialized methods for restricted graph classes, in particular for those classes with arguable practical significance such as planar graphs and complex networks.

/pdf/shortest-path-queries-in-static-networks-t3dlcej7at.pdf

Shortest-path queries in static networks

Considerable amounts of data, including process events, are collected and stored by organisations nowadays. Discovering a process model from such event data and verification of the quality of discovered models are important steps in process mining. Many discovery techniques have been proposed, but none of them combines scalability with strong quality guarantees. We would like such techniques to handle billions of events or thousands of activities, to produce sound models (without deadlocks and other anomalies), and to guarantee that the underlying process can be rediscovered when sufficient information is available. In this paper, we introduce a framework for process discovery that ensures these properties while passing over the log only once and introduce three algorithms using the framework. To measure the quality of discovered models for such large logs, we introduce a model–model and model–log comparison framework that applies a divide-and-conquer strategy to measure recall, fitness, and precision. We experimentally show that these discovery and measuring techniques sacrifice little compared to other algorithms, while gaining the ability to cope with event logs of 100,000,000 traces and processes of 10,000 activities on a standard computer.

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Scalable process discovery and conformance checking

Process compliance measurement is getting increasing attention in companies due to stricter legal requirements and market pressure for operational excellence. In order to judge on compliance of the business processing, the degree of behavioural deviation of a case, i.e., an observed execution sequence, is quantified with respect to a process model (referred to as fitness, or recall). Recently, different compliance measures have been proposed. Still, nearly all of them are grounded on state-based techniques and the trace equivalence criterion, in particular. As a consequence, these approaches have to deal with the state explosion problem. In this paper, we argue that a behavioural abstraction may be leveraged to measure the compliance of a process log – a collection of cases. To this end, we utilise causal behavioural profiles that capture the behavioural characteristics of process models and cases, and can be computed efficiently. We propose different compliance measures based on these profiles, discuss the impact of noise in process logs on our measures, and show how diagnostic information on non-compliance is derived. As a validation, we report on findings of applying our approach in a case study with an international service provider.

Process compliance analysis based on behavioural profiles

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.

/pdf/fast-fully-dynamic-landmark-based-estimation-of-shortest-2hyydny28x.pdf

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

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.

/pdf/online-conformance-checking-using-behavioural-patterns-4ey7cpyr86.pdf

Online conformance checking using behavioural patterns

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.

/pdf/behavioral-comparison-of-process-models-based-on-canonically-4c32afrkdn.pdf

Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures

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.

/pdf/scalable-conformance-checking-of-business-processes-3wtlkevc1v.pdf

Abel Armas-Cervantes

Papers

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

Online conformance checking using behavioural patterns

Behavioral Comparison of Process Models Based on Canonically Reduced Event Structures

Scalable Conformance Checking of Business Processes

Diagnosing behavioral differences between business process models