In this work, we study longest common substring, pattern matching, and wildcard pattern matching in the asymmetric streaming model. In this streaming model, we have random access to one string and streaming access to the other one. We present streaming algorithms with provable guarantees for these three fundamental problems. In particular, our algorithms for pattern matching improve the upper bound and beat the unconditional lower bounds on the memory of randomized and deterministic streaming algorithms. In addition to this, we present algorithms for wildcard pattern matching in the asymmetric streaming model that have optimal space and time.

翻译：在这项工作中,我们研究不对称流模式中最长的共同子字符串、图案匹配和通配符模式。在这个流模式中,我们随机访问一个字符串和流存访问另一个。我们提出流算法,为这三个基本问题提供可证实的保证。特别是,我们用于模式匹配的算法改进了上层框,并击败了随机和确定性流算法记忆中的无条件下限。除此之外,我们还提出了具有最佳空间和时间的不对称流算法模式中的通配算法。