On the numerical representation of labeled graphs with self-loops

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    2 Citations (Scopus)

    Abstract

    Graphs with self-loops enable to represent a large variety of interactions in natural and artificial systems, allowing not only inter-connectivity among heterogeneous entities but also the self-dependence of entities, e.g.The recursive and autonomous nature of dynamical systems. In this paper we present new bijective constructs which enable the numerical representation of graphs with self loops (or loopy graphs). In particular, we study the case of (1) undirected and (2) directed graphs with n nodes and m edges with self-loops. Our proposed approach realizes the succinct representations by using integer numbers in which rigorous computational experiments show the efficiency of our proposed algorithms: The complexity follows a quasi-linear behaviour as a function of the number of edges (which is independent of the number of nodes). Furthermore, as direct consequence of our constructs, we propose list structures having O(m) space complexity, which realize the linear space complexity depending only on the number of edges (the list is independent of n). We believe that our bijective algorithms are useful to tackle problems involving sampling of graphical models, network design as well as process planning by using number theory and sample-based learning.

    Original languageEnglish
    Title of host publicationProceedings - 2017 International Conference on Tools with Artificial Intelligence, ICTAI 2017
    PublisherIEEE Computer Society
    Pages342-349
    Number of pages8
    Volume2017-November
    ISBN (Electronic)9781538638767
    DOIs
    Publication statusPublished - 2018 Jun 4
    Event29th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2017 - Boston, United States
    Duration: 2017 Nov 62017 Nov 8

    Other

    Other29th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2017
    CountryUnited States
    CityBoston
    Period17/11/617/11/8

    Keywords

    • Graph representation
    • Labeled graphs
    • Numerical representation
    • Optimization

    ASJC Scopus subject areas

    • Software
    • Artificial Intelligence
    • Computer Science Applications

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  • Cite this

    Parque Tenorio, V., & Miyashita, T. (2018). On the numerical representation of labeled graphs with self-loops. In Proceedings - 2017 International Conference on Tools with Artificial Intelligence, ICTAI 2017 (Vol. 2017-November, pp. 342-349). IEEE Computer Society. https://doi.org/10.1109/ICTAI.2017.00061