We consider the problem of doing fast and reliable estimation of the number of non-zero entries in a sparse boolean matrix product. Let n denote the total number of non-zero entries in the input matrices. We show how to compute a 1±ε approximation (with small probability of error) in expected time O(n) for any ε > 4√n. The previously best estimation algorithm, due to Cohen (JCSS 1997), uses time O(n/ε2. We also present a variant using O(sort(n)) I/Os in expectation in the cache-oblivious model. We also describe how sampling can be used to maintain (independent) sketches of matrices that allow estimation to be performed in time o(n) if z is sufficiently large. This gives a simpler alternative to the sketching technique of Ganguly et al. (PODS 2005), and matches a space lower bound shown in that paper. © 2010 Springer-Verlag.
CITATION STYLE
Amossen, R. R., Campagna, A., & Pagh, R. (2010). Better size estimation for sparse matrix products. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6302 LNCS, pp. 406–419). https://doi.org/10.1007/978-3-642-15369-3_31
Mendeley helps you to discover research relevant for your work.