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Adjacency Relation

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Akhil Kumar – One of the best experts on this subject based on the ideXlab platform.

  • transition Adjacency Relation computation based on unfolding potentials and challenges
    OTM Confederated International Conferences "On the Move to Meaningful Internet Systems", 2016
    Co-Authors: Xiaojun Ye, Akhil Kumar

    Abstract:

    Transition Adjacency Relation (TAR) has provided a useful perspective for process model similarity measurement. Motivated by recent developments of other similarity metrics, this article puts TAR computation in the context of Petri net unfolding. Apart from being significantly faster than existing TAR computation algorithms, unfolding-based TAR computation also provides the potentials of enhancement through combination with other metrics that can be obtained from unfolding, especially the popular Behavior Profiles. We show that TAR computation can generally be reduced to coverability problem and solved using unfolding. However, there are also questions to be answered regarding how to further exploit unfolding information for optimal efficiency and handle silent transitions. In this article, we discuss what has been learned from our research, and also point out the open issues.

  • OTM Conferences – Transition Adjacency Relation Computation Based on Unfolding: Potentials and Challenges
    On the Move to Meaningful Internet Systems: OTM 2016 Conferences, 2016
    Co-Authors: Xiaojun Ye, Akhil Kumar

    Abstract:

    Transition Adjacency Relation (TAR) has provided a useful perspective for process model similarity measurement. Motivated by recent developments of other similarity metrics, this article puts TAR computation in the context of Petri net unfolding. Apart from being significantly faster than existing TAR computation algorithms, unfolding-based TAR computation also provides the potentials of enhancement through combination with other metrics that can be obtained from unfolding, especially the popular Behavior Profiles. We show that TAR computation can generally be reduced to coverability problem and solved using unfolding. However, there are also questions to be answered regarding how to further exploit unfolding information for optimal efficiency and handle silent transitions. In this article, we discuss what has been learned from our research, and also point out the open issues.

  • Efficient Transition Adjacency Relation Computation for Process Model Similarity
    IEEE Transactions on Services Computing, 1
    Co-Authors: Xiaojun Ye, Akhil Kumar

    Abstract:

    Many activities in business process management, such as process retrieval, process mining and process integration, need to determine the similarity between business processes. Along with many other Relational behavior semantics, Transition Adjacency Relation (abbr. TAR) has been proposed as a kind of behavioral gene of process models and a useful perspective for process similarity measurement. In this article we explain why it is still relevant and necessary to improve TAR or pTAR (i.e., projected TAR) computation efficiency and put forward a novel approach for TAR computation based on Petri net unfolding. This approach not only improves the efficiency of TAR computation, but also enables the long-expected combined usage of TAR and Behavior Profiles (abbr. BP) in process model similarity estimation.

Xiaojun Ye – One of the best experts on this subject based on the ideXlab platform.

  • transition Adjacency Relation computation based on unfolding potentials and challenges
    OTM Confederated International Conferences "On the Move to Meaningful Internet Systems", 2016
    Co-Authors: Xiaojun Ye, Akhil Kumar

    Abstract:

    Transition Adjacency Relation (TAR) has provided a useful perspective for process model similarity measurement. Motivated by recent developments of other similarity metrics, this article puts TAR computation in the context of Petri net unfolding. Apart from being significantly faster than existing TAR computation algorithms, unfolding-based TAR computation also provides the potentials of enhancement through combination with other metrics that can be obtained from unfolding, especially the popular Behavior Profiles. We show that TAR computation can generally be reduced to coverability problem and solved using unfolding. However, there are also questions to be answered regarding how to further exploit unfolding information for optimal efficiency and handle silent transitions. In this article, we discuss what has been learned from our research, and also point out the open issues.

  • OTM Conferences – Transition Adjacency Relation Computation Based on Unfolding: Potentials and Challenges
    On the Move to Meaningful Internet Systems: OTM 2016 Conferences, 2016
    Co-Authors: Xiaojun Ye, Akhil Kumar

    Abstract:

    Transition Adjacency Relation (TAR) has provided a useful perspective for process model similarity measurement. Motivated by recent developments of other similarity metrics, this article puts TAR computation in the context of Petri net unfolding. Apart from being significantly faster than existing TAR computation algorithms, unfolding-based TAR computation also provides the potentials of enhancement through combination with other metrics that can be obtained from unfolding, especially the popular Behavior Profiles. We show that TAR computation can generally be reduced to coverability problem and solved using unfolding. However, there are also questions to be answered regarding how to further exploit unfolding information for optimal efficiency and handle silent transitions. In this article, we discuss what has been learned from our research, and also point out the open issues.

  • Computation of Transition Adjacency Relations Based on Complete Prefix Unfolding (Technical Report)
    arXiv: Other Computer Science, 2015
    Co-Authors: Xiaojun Ye

    Abstract:

    An increasing number of works have devoted to the application of Transition Adjacency Relation (TAR) as a means to capture behavioral features of business process models. In this paper, we systematically study the efficient TAR derivation from process models using unfolding technique which previously has been used to address the state space explosion when dealing with concurrent behaviors of a Petri net. We reveal and formally describe the equivalence between TAR and Event Adjacency Relation (EAR), the manifestation of TAR in the Complete Prefix Unfolding (CPU) of a Petri net. By computing TARs from CPU using this equivalence, we can alleviate the concurrency caused state-explosion issues. Furthermore, structural boosting rules are categorized, proved and added to the TAR computing algorithm. Formal proofs of correctness and generality of CPU-based TAR computation are provided for the first time by this work, and they significantly expand the range of Petri nets from which TARs can be efficiently derived. Experiments on both industrial and synthesized process models show the effectiveness of proposed CPU-based algorithms as well as the observation that they scale well with the increase in size and concurrency of business process models.

Alexandre Xavier Falcão – One of the best experts on this subject based on the ideXlab platform.

  • An Iterative Spanning Forest Framework for Superpixel Segmentation
    IEEE Transactions on Image Processing, 2019
    Co-Authors: John E. Vargas-muñoz, Felipe Lemes Galvão, Ananda Shankar Chowdhury, Eduardo B. Alexandre, Paulo Vechiatto A. Miranda, Alexandre Xavier Falcão

    Abstract:

    Superpixel segmentation has emerged as an important research problem in the areas of image processing and computer vision. In this paper, we propose a framework, namely Iterative Spanning Forest (ISF), in which improved sets of connected superpixels (supervoxels in 3D) can be generated by a sequence of image foresting transforms. In this framework, one can choose the most suitable combination of ISF components for a given application-i.e., 1) a seed sampling strategy; 2) a connectivity function; 3) an Adjacency Relation; and 4) a seed pixel recomputation procedure. The superpixels in ISF structurally correspond to spanning trees rooted at those seeds. We present five ISF-based methods to illustrate different choices for those components. These methods are compared with a number of state-of-the-art approaches with respect to effectiveness and efficiency. Experiments are carried out on several datasets containing 2D and 3D objects with distinct texture and shape properties, including a high-level application, named sky image segmentation. The theoretical properties of ISF are demonstrated in the supplementary material and the results show ISF-based methods rank consistently among the best for all datasets.

  • RISF: Recursive Iterative Spanning Forest for Superpixel Segmentation
    2018 31st SIBGRAPI Conference on Graphics Patterns and Images (SIBGRAPI), 2018
    Co-Authors: Felipe Lemes Galvão, Alexandre Xavier Falcão, Ananda Shankar Chowdhury

    Abstract:

    Methods for superpixel segmentation have become very popular in computer vision. Recently, a graph-based framework named ISF (Iterative Spanning Forest) was proposed to obtain connected superpixels (supervoxels in 3D) based on multiple executions of the Image Foresting Transform (IFT) algorithm from a given choice of four components: a seed sampling strategy, an Adjacency Relation, a connectivity function, and a seed recomputation procedure. In this paper, we extend ISF to introduce a unique characteristic among superpixel segmentation methods. Using the new framework, termed as Recursive Iterative Spanning Forest (RISF), one can recursively generate multiple segmentation scales on region Adjacency graphs (i.e., a hierarchy of superpixels) without sacrificing the efficiency and effectiveness of ISF. In addition to a hierarchical segmentation, RISF allows a more effective geodesic seed sampling strategy, with no negative impact in the efficiency of the method. For a fixed number of scales using 2D and 3D image datasets, we show that RISF can consistently outperform the most competitive ISF-based methods.