Since its introduction, the level set method has become the favorite technique for capturing and tracking moving interfaces, and found applications in a wide variety of scientific fields. In this paper we present efficient data structures and algorithms for tracking dynamic interfaces through the level set method. Several approaches which address both computational and memory requirements have been very recently introduced. We show that our method is up to 8.5 times faster than these recent approaches. More importantly, our algorithm can greatly benefit from both fine- and coarse-grain parallelization by leveraging SIMD and/or multi-core parallel architectures.