10.4230/LIPICS.STACS.2008.1341
Brody, Joshua
Joshua
Brody
Chakrabarti, Amit
Amit
Chakrabarti
Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2008
Communication complexity
pointer jumping
number on the forehead
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
2008
2008-02-06
2008-02-06
2008-02-06
en
urn:nbn:de:0030-drops-13415
10.4230/LIPIcs.STACS.2008
978-3-939897-06-4
1868-8969
10.4230/LIPIcs.STACS.2008
LIPIcs, Volume 1, STACS 2008
25th International Symposium on Theoretical Aspects of Computer Science
2013
1
14
145
156
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Albers, Susanne
Susanne
Albers
Weil, Pascal
Pascal
Weil
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2008
1
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
195979 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
We study the one-way number-on-the-forehead (NOF) communication
complexity of the $k$-layer pointer jumping problem with $n$
vertices per layer. This classic problem, which has connections to
many aspects of complexity theory, has seen a recent burst of
research activity, seemingly preparing the ground for an
$Omega(n)$ lower bound, for constant $k$. Our first result is a
surprising sublinear --- i.e., $o(n)$ --- upper bound for the
problem that holds for $k ge 3$, dashing hopes for such a lower
bound.
A closer look at the protocol achieving the upper bound shows that
all but one of the players involved are collapsing, i.e., their
messages depend only on the composition of the layers ahead of
them. We consider protocols for the pointer jumping problem where
all players are collapsing. Our second result shows that a strong
$n - O(log n)$ lower bound does hold in this case. Our third
result is another upper bound showing that nontrivial protocols for
(a non-Boolean version of) pointer jumping are possible even when
all players are collapsing.
Our lower bound result uses a novel proof technique, different from
those of earlier lower bounds that had an information-theoretic
flavor. We hope this is useful in further study of the problem.
LIPIcs, Vol. 1, 25th International Symposium on Theoretical Aspects of Computer Science, pages 145-156