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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND
verfasst von : T. S. Jayram
Erschienen in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Verlag: Springer Berlin Heidelberg
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The
${\textsc{And}}$
problem on
t
bits is a promise decision problem where either at most one bit of the input is set to 1 (
No
instance) or all
t
bits are set to 1 (
${\textsc{Yes}}$
instance). In this note, I will give a new proof of an Ω(1/
t
) lower bound on the information complexity of
${\textsc{And}}$
in the number-in-hand model of communication. This was recently established by Gronemeier, STACS 2009. The proof exploits the information geometry of communication protocols via Hellinger distance in a novel manner and avoids the analytic approach inherent in previous work. As previously known, this bound implies an Ω(
n
/
t
) lower bound on the communication complexity of multiparty disjointness and consequently a Ω(
n
1 − 2/
k
) space lower bound on estimating the
k
-th frequency moment
F
k
.