An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance
نویسندگان
چکیده
منابع مشابه
The Communication Complexity of Gap Hamming Distance
In the gap Hamming distance problem, two parties must determine whether their respective strings x; y 2 f0; 1g are at Hamming distance less than n=2 p n or greater than n=2 C p n: In a recent tour de force, Chakrabarti and Regev (STOC ’11) proved the long-conjectured ̋.n/ bound on the randomized communication complexity of this problem. In follow-up work several months ago, Vidick (2010; ECCC T...
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In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem (GHDnL,U ): Alice and Bob are given binary string of length n and they are guaranteed that Hamming distance between their inputs is either ≤ L or ≥ U for some L < U . They have to output 0, if the first inequality holds, and 1, if the second inequality holds. In this paper we study the communication ...
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Assume that Alice has a binary string x and Bob a binary string y, both of length n. Their goal is to output 0, if x and y are at least Lclose in Hamming distance, and output 1, if x and y are at least U -far in Hamming distance, where L < U are some integer parameters known to both parties. If the Hamming distance between x and y lies in the interval (L, U), they are allowed to output anything...
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Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on at most a bits? Let 0 ≤ a ≤ n − 1. We show that any deterministic protocol, as well as any error-free quantum protocol (C∗ version), for this problem requires at least n− 2 bits of communication. We show the same bounds for the problem of determining if two strings differ in exactly a bits. We als...
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We investigate the randomized and quantum communication complexity of the HAMMING DISTANCE problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of (d) qubits in the general interactive model with shared prior entanglement. We also construct a classical protocol of O(d logd) bits in the restricted Simultane...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2012
ISSN: 0097-5397,1095-7111
DOI: 10.1137/120861072