Two Player Hidden Pointer Chasing and Multi-Pass Lower Bounds in Turnstile Streams
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The authors have withdrawn this paper due to an error in the proof of Lemma 3.4. ——————————————————————————————– The authors have withdrawn this paper due to an error in the proof of Lemma 3.4z(Assadi, Chen, and Khanna, 2019) define a 4-player hidden-pointer-chasing (𝖧𝖯𝖢^4), and using it, give strong multi-pass lower bounds for graph problems in the streaming model of computation and a lower bound on the query complexity of sub-modular minimization. We present a two-player version (𝖧𝖯𝖢^2) of 𝖧𝖯𝖢^4 that has matching communication complexity to 𝖧𝖯𝖢^4. Our formulation allows us to lower bound its communication complexity with a simple direct-sum argument. Using this lower bound on the communication complexity of 𝖧𝖯𝖢^2, we retain the streaming and query complexity lower bounds by (Assadi, Chen, and Khanna, 2019). Further, by giving reductions from 𝖧𝖯𝖢^2, we prove new multi-pass space lower bounds for graph problems in turnstile streams. In particular, we show that any algorithm which computes the exact weight of the maximum weighted matching in an n-vertex graph requires Õ(n^2) space unless it makes ω(log n) passes over the turnstile stream, and that any algorithm which computes the minimum s-t distance in an n-vertex graph requires n^2-o(1) space unless it makes n^Ω(1) passes over the turnstile stream. Our reductions can be modified to use 𝖧𝖯𝖢^4 as well.
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