International Journal Papers

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Author: search.filters.author.Kheddouci, Hamamache

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    Fast parallel algorithms for finding elementary circuits of a directed graph: a GPU-based approach
    (Springer Science+Business Media, 2023-03) Benachour, Amira; Yahiaoui, Saïd; El Baz, Didier; Nouali‑Taboudjemat, Nadia; Kheddouci, Hamamache
    Circuits in a graph are interesting structures and identifying them is of an important relevance for many applications. However, enumerating circuits is known to be a difficult problem, since their number can grow exponentially. In this paper, we propose fast parallel approaches for enumerating elementary circuits of directed graphs based on graphics processing unit (GPU). Our algorithms are based on a massive exploration of the graph in a breadth-first search strategy. Algorithm V-FEC explores the graph starting from different vertices simultaneously. To further reduce the search space, we present T-FEC, another algorithm that uses triplets as an initial set to start exploring. To the best of our knowledge, those are the first parallel GPU-based algorithms for finding all circuits of a given graph. In addition, they find circuits of a given length and circuits with a specific vertex or edge. The evaluation results show that the proposed approaches achieve up to 190x speed-up over Johnson’s algorithm, one of the most efficient sequential algorithms for finding circuits.
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    Coloring based approach for matching unrooted and/or unordered trees
    (Elsevier, 2013-04) Yahiaoui, Saïd; Haddad, Mohammed; Effantin, Brice; Kheddouci, Hamamache
    We consider the problem of matching unrooted unordered labeled trees, which refers to the task of evaluating the distance between trees. One of the most famous formalizations of this problem is the computation of the edit distance defined as the minimum-cost sequence of edit operations that transform one tree into another. Unfortunately, this problem has been proved to be NP-complete. In this paper, we propose a new algorithm to measure distance between unrooted unordered labeled trees. This algorithm uses a specific graph coloring to decompose the trees into small components (stars and bistars). Then, it determines a distance between two trees by computing the edit distance between their components. We prove that the proposed distance is a pseudo-metric and we analyze its time complexity. Our experimental evaluations on large synthetic and real world datasets confirm our analytical results and suggest that the distance we propose is accurate and its algorithm is scalable.
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    A Survey on Distributed Graph Pattern Matching in Massive Graphs
    (ACM, 2021-02) Bouhenni, Sarra; Yahiaoui, Saïd; Nouali-Taboudjemat, Nadia; Kheddouci, Hamamache
    Besides its NP-completeness, the strict constraints of subgraph isomorphism are making it impractical for graph pattern matching (GPM) in the context of big data. As a result, relaxed GPM models have emerged as they yield interesting results in a polynomial time. However, massive graphs generated by mostly social networks require a distributed storing and processing of the data over multiple machines, thus, requiring GPM to be revised by adopting new paradigms of big graphs processing, e.g., Think-Like-A-Vertex and its derivatives. This article discusses and proposes a classification of distributed GPM approaches with a narrow focus on the relaxed models.
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    Distributed graph pattern matching via bounded dual simulation
    (Elsevier, 2022-09) Bouhenni, Sarra; Yahiaoui, Saïd; Nouali-Taboudjemat, Nadia; Kheddouci, Hamamache
    Graph Pattern Matching (GPM) finds subgraphs of a large data graph that are similar to an input query graph. It has many applications, such as pattern recognition, detecting plagiarism, and finding communities in social networks. Current real-world applications generate massive amounts of data that cannot be stored on the memory of a single machine, which raises the need for distributed storage and processing. Recent relaxed GPM models, although of polynomial time complexity, are nevertheless not distributed by nature. Moreover, the existing relaxed GPM algorithms are limited in terms of scalability. In this paper, we propose Bounded Dual Simulation (BDSim) as a new relaxed model for a scalable evaluation of GPM in massive graphs. BDSim captures more semantic similarities compared to graph simulation, dual simulation, and even strong simulation. It preserves the vertices’ proximity by eliminating cycles of unbounded length from the resulting match graph. Furthermore, we propose distributed vertex-centric algorithms to evaluate BDSim. We prove their effectiveness and efficiency through detailed theoretical validation and extensive experiments conducted on real-world and synthetic datasets. To the best of our knowledge, BDSim is the first relaxed GPM model that captures the cyclic structure of the query graph while being feasible in cubic time.
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    Efficient self-stabilizing algorithms for minimal total k-dominating sets in graphs
    (Elsevier, 2014-07) Belhoul, Yacine; Yahiaoui, Saïd; Kheddouci, Hamamache
    We propose the first polynomial self-stabilizing distributed algorithm for the minimal total dominating set problem in an arbitrary graph. Then, we generalize the proposed algorithm for the minimal total k -dominating set problem. Under an unfair distributed scheduler, the proposed algorithms converge in O(mn) moves starting from any arbitrary state, and require O(log n) storage per node.