The communication complexity of the Hamming distance problem
نویسندگان
چکیده
منابع مشابه
The communication complexity of the Hamming distance problem
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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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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Consider the following version of the Hamming distance problem for ±1 vectors of length n: the promise is that the distance is either at least 2 + √ n or at most 2 − √ n, and the goal is to find out which of these two cases occurs. Woodruff (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2004) gave a linear lower bound for the randomized one-way communication complexity of this problem. In th...
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The Hamming distance function Hamn,d returns 1 on all pairs of inputs x and y that differ in at most d coordinates and returns 0 otherwise. We initiate the study of the information complexity of the Hamming distance function. We give a new optimal lower bound for the information complexity of the Hamn,d function in the small-error regime where the protocol is required to err with probability at...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2006
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2006.01.014