Cache-Oblivious Peeling of Random Hypergraphs

Djamal Belazzougui; Paolo Boldi; Giuseppe Ottaviano; Rossano Venturini; Sebastiano Vigna

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arXiv · 1312.0526

Cache-Oblivious Peeling of Random Hypergraphs

Djamal Belazzougui·Paolo Boldi·Giuseppe Ottaviano·Rossano Venturini·Sebastiano Vigna

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Abstract

The computation of a peeling order in a randomly generated hypergraph is the most time-consuming step in a number of constructions, such as perfect hashing schemes, random $r$-SAT solvers, error-correcting codes, and approximate set encodings. While there exists a straightforward linear time algorithm, its poor I/O performance makes it impractical for hypergraphs whose size exceeds the available internal memory. We show how to reduce the computation of a peeling order to a small number of sequential scans and sorts, and analyze its I/O complexity in the cache-oblivious model. The resulting algorithm requires $O(\mathrm{sort}(n))$ I/Os and $O(n \log n)$ time to peel a random hypergraph with $n$ edges. We experimentally evaluate the performance of our implementation of this algorithm in a real-world scenario by using the construction of minimal perfect hash functions (MPHF) as our test case: our algorithm builds a MPHF of $7.6$ billion keys in less than $21$ hours on a single machine. The resulting data structure is both more space-efficient and faster than that obtained with the current state-of-the-art MPHF construction for large-scale key sets.

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Djamal Belazzougui, Paolo Boldi, Giuseppe Ottaviano, Rossano Venturini, Sebastiano Vigna. 2013-12-02. Cache-Oblivious Peeling of Random Hypergraphs. https://arxiv.org/abs/1312.0526

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