2006 | OriginalPaper | Buchkapitel
The Multiparty Communication Complexity of Exact-T: Improved Bounds and New Problems
verfasst von : Richard Beigel, William Gasarch, James Glenn
Erschienen in: Mathematical Foundations of Computer Science 2006
Verlag: Springer Berlin Heidelberg
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Let
x
i
,...,
x
k
be
n
-bit numbers and
T
∈ ℕ. Assume that
P
1
,...,
P
k
are players such that
P
i
knows all of the numbers
exceptx
i
. They want to determine if
$\sum^{k}_{j=1}{\it x}_{j}$
=
T
by broadcasting as few bits as possible. In [7] an upper bound of
$O(\sqrt n )$
bits was obtained for the
k
=3 case, and a lower bound of
ω
(1) for
k
≥3 when
T
=Θ(2
n
). We obtain (1) for
k
≥3 an upper bound of
$k+O((n+\log k)^{1/(\lfloor{\rm lg(2k-2)}\rfloor)})$
, (2) for
k
=3,
T
=Θ(2
n
), a lower bound of Ω(loglog
n
), (3) a generalization of the protocol to abelian groups, (4) lower bounds on the multiparty communication complexity of some regular languages, and (5) empirical results for
k
= 3.