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    A color-avoiding approach to subgraph counting in Bounded Expansion Classes

    Reidl, Felix and Sullivan, B. (2023) A color-avoiding approach to subgraph counting in Bounded Expansion Classes. Algorithmica 85 (8), pp. 2318-2347. ISSN 0178-4617.

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    We present an algorithm to count the number of occurrences of a pattern graph H on h vertices as an induced subgraph in a host graph G. If G belongs to a bounded expansion class, the algorithm runs in linear time, if G belongs to a nowhere dense class it runs in almost-linear time. Our design choices are motivated by the need for an approach that can be engineered into a practical implementation for sparse host graphs. Specifically, we introduce a decomposition of the pattern H called a counting dag which encodes an order-aware, inclusion-exclusion counting method for H. Given such a counting dag and a suitable linear ordering of G as input, our algorithm can count the number of times H appears as an induced subgraph in G in time , where denotes the maximum size of the weakly h-reachable sets in . This implies, combined with previous results, an algorithm with running time which only takes H and G as input. We note that with a small modification, our algorithm can instead use strongly h-reachable sets with running time , resulting in an overall complexity of when only given H and G. Because orderings with small weakly/strongly reachable sets can be computed relatively efficiently in practice (Nadara et al.: in J Exp Algorithmics 103:14:1–14:16, 2018), our algorithm provides a promising alternative to algorithms using the traditional p-treedepth coloring framework (O’Brien and Sullivan in: Experimental evaluation of counting subgraph isomorphisms in classes of bounded expansion, CoRR, arXiv:1712.06690, 2017). We describe preliminary experimental results from an initial open source implementation which highlight its potential.


    Item Type: Article
    Keyword(s) / Subject(s): Sparse graphs, Subgraph counting, Bounded expansion, Weak coloring number, Strong coloring number
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Felix Reidl
    Date Deposited: 06 Nov 2023 16:52
    Last Modified: 03 Feb 2024 01:10


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