Abstract
In this work, we explore the application of sketching data structures to solve problems in graphs that do not fit entirely in memory. These structures allow compact representations of data, admitting some probability of failure. We aim at the implicit representation and dynamic connectivity problems. Our contributions include two new probabilistic implicit representations, one that uses Bloom filters and allows representing sparse graphs with O(|E|) bits, and another that uses MinHash sketches and represents trees with O(|V|) bits. We also describe a variant of an \(\ell _0\)-sampling sketch that allows proving a tighter upper bound on the failure probability of sampling.
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The authors acknowledge partial financial support from CNPq, CAPES, and a FAPERJ BBP grant.
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Lopes, J.P.A., Oliveira, F.S., Pinto, P.E.D., Barbosa, V.C. (2019). Sketching Data Structures for Massive Graph Problems. In: Gadepally, V., Mattson, T., Stonebraker, M., Wang, F., Luo, G., Teodoro, G. (eds) Heterogeneous Data Management, Polystores, and Analytics for Healthcare. DMAH Poly 2018 2018. Lecture Notes in Computer Science(), vol 11470. Springer, Cham. https://doi.org/10.1007/978-3-030-14177-6_5
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