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We consider the problem of dictionary matching in a stream. Given a set of strings, known as a dictionary, and a stream of characters arriving one at a time, the task is to report each time some string in our dictionary occurs in the stream. We present a randomised algorithm which takes O(log log(k + m)) time per arriving character and uses O(k log m) words of space, where k is the number of strings in the dictionary and m is the length of the longest string in the dictionary.
The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream
We consider the problem of computing a $(1+epsilon)$-approximation of the Hamming distance between a pattern of length $n$ and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem, giving
We propose a formal graph-theoretic model for studying the problem of matching rides online in a ride-sharing platform. Unlike most of the literature on online matching, our model, that we call {em Online Windowed Non-Bipartite Matching} ($mbox{OWNBM
We consider several types of internal queries: questions about subwords of a text. As the main tool we develop an optimal data structure for the problem called here internal pattern matching. This data structure provides constant-time answers to quer
We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so t