188 research outputs found

    Improved Bounds for Matching in Random-Order Streams

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    Almost Optimal Distribution-Free Junta Testing

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    We consider the problem of testing whether an unknown n-variable Boolean function is a k-junta in the distribution-free property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability distribution over {0,1}^n. Chen, Liu, Servedio, Sheng and Xie [Zhengyang Liu et al., 2018] showed that the distribution-free k-junta testing can be performed, with one-sided error, by an adaptive algorithm that makes O~(k^2)/epsilon queries. In this paper, we give a simple two-sided error adaptive algorithm that makes O~(k/epsilon) queries

    Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms

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    We prove that any two-pass graph streaming algorithm for the ss-tt reachability problem in nn-vertex directed graphs requires near-quadratic space of n2−o(1)n^{2-o(1)} bits. As a corollary, we also obtain near-quadratic space lower bounds for several other fundamental problems including maximum bipartite matching and (approximate) shortest path in undirected graphs. Our results collectively imply that a wide range of graph problems admit essentially no non-trivial streaming algorithm even when two passes over the input is allowed. Prior to our work, such impossibility results were only known for single-pass streaming algorithms, and the best two-pass lower bounds only ruled out o(n7/6)o(n^{7/6}) space algorithms, leaving open a large gap between (trivial) upper bounds and lower bounds

    Finding an Optimal Alphabet Ordering for Lyndon Factorization Is Hard

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    Space Optimal Vertex Cover in Dynamic Streams

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