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oai:drops-oai.dagstuhl.de:1341 2024-03-06T10:32:57Z ddc:004 open_access

Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound Brody, Joshua Chakrabarti, Amit Communication complexity pointer jumping number on the forehead 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Joshua Brody and Amit Chakrabarti 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1341 urn:nbn:de:0030-drops-13415 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1341 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode