eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
7:1
7:15
10.4230/LIPIcs.MFCS.2018.7
article
One-Sided Error Communication Complexity of Gap Hamming Distance
Klenin, Egor
1
Kozachinskiy, Alexander
2
https://orcid.org/0000-0002-9956-9023
Lomonosov Moscow State University, Moscow, Russia, Moscow, 1 Leninskiye Gory, Russia
National Research University Higher School of Economics, Moscow, Russia, Moscow, 3 Kochnovsky Proezd, Russia
Assume that Alice has a binary string x and Bob a binary string y, both strings are of length n. Their goal is to output 0, if x and y are at least L-close 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. This problem is called the Gap Hamming Distance. In this paper we study public-coin one-sided error communication complexity of this problem. The error with probability at most 1/2 is allowed only for pairs at Hamming distance at least U. In this paper we determine this complexity up to factors logarithmic in L. The protocol we construct for the upper bound is simultaneous.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.7/LIPIcs.MFCS.2018.7.pdf
Communication Complexity
Gap Hamming Distance
one-sided error