Recent advances in long-read sequencing enable the characterization of genome structure and its intra-and inter-species variation at a resolution that was previously impossible. Detecting overlaps between reads is integral to many long-read genomics pipelines, such as de novo genome assembly. While longer reads simplify genome assembly and improve the contiguity of the reconstruction, current long-read technologies come with high error rates. We present Berkeley Long-Read to Long-Read Aligner and Overlapper (BELLA), a novel algorithm for computing overlaps and alignments via sparse matrix-matrix multiplication that balances the goals of recall and precision, performing well on both.We present a probabilistic model that demonstrates the feasibility of using short k-mers for detecting candidate overlaps. We then introduce a notion of reliable k-mers based on our probabilistic model. Combining reliable k-mers with our binning mechanism eliminates both the k-mer set explosion that would otherwise occur with highly erroneous reads, and the spurious overlaps from k-mers originating in repetitive regions. Finally, we present a new method based on Chernoff bounds for separating true overlaps from false positives using a combination of alignment techniques and probabilistic modeling. Our methodologies aim at maximizing the balance between precision and recall. On both real and synthetic data, BELLA performs amongst the best in terms of F1 score, showing a performance stability which is often missing for competitor software. BELLA's F1 score is consistently within 1.7% of the top entry. Notably, we show improved de novo assembly results on synthetic data when coupling BELLA with the Miniasm assembler.Long-read technologies (Eid et al., 2009;Goodwin et al., 2015) generate long reads with average lengths reaching and often exceeding 10,000 base pairs (bp). These allow the resolution of complex genomic repetitions, enabling more accurate ensemble views that were not possible with previous short-read technologies (Phillippy et al., 2008;Nagarajan and Pop, 2009). However, the improved read length of these technologies comes at the cost of lower accuracy, with error rates ranging from 5% to 35%. Nevertheless, errors are more random and more evenly distributed within Pacific Biosciences long-read data (Giordano et al., 2017) compared to short-read technologies.The majority of the state-of-the-art long-read assemblers uses the Overlap-Layout-Consensus (OLC) paradigm (Berlin et al., 2015). The first step in OLC assembly consists of detecting overlaps between reads to construct an overlap (or string) graph. The OLC paradigm benefits from longer reads as significantly fewer reads are required to cover the genome, limiting the size of the overlap graph. Highly-accurate overlap detection is a major computational bottleneck in OLC assembly (Myers, 2014), mainly due to the compute-intensive nature of pairwise alignment.At present, several algorithms are capable of overlapping error-prone long-read data with varying accuracy. The prevaili...