Sublinear Communication Protocols for Multi-Party Pointer Jumping and a Related Lower Bound

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 (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 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 eve...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Joshua Brody, Amit Chakrabarti
• Keywords: CORR 2008, Education, K-layer Pointer, Lower Bounds, Upper Bound