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In this work, we study longest common substring, pattern matching, andwildcard pattern matching in the asymmetric streaming model. In this streamingmodel, we have random access to one string and streaming access to the otherone. We present streaming algorithms with provable guarantees for these threefundamental problems. In particular, our algorithms for pattern matchingimprove the upper bound and beat the unconditional lower bounds on the memoryof randomized and deterministic streaming algorithms. In addition to this, wepresent algorithms for wildcard pattern matching in the asymmetric streamingmodel that have optimal space and time.

Optimal Space and Time for Streaming Pattern Matching