We present novoBreak, a genome-wide local assembly algorithm that discovers somatic and germline structural variation breakpoints in whole-genome sequencing data. novoBreak consistently outperformed existing algorithms on real cancer genome data and on synthetic tumors in the ICGC-TCGA DREAM 8.5 Somatic Mutation Calling Challenge primarily because it more effectively utilized reads spanning breakpoints. novoBreak also demonstrated great sensitivity in identifying short insertions and deletions.