We introduce the model of conservative one-way multiparty complexity
and prove lower and upper bounds on the complexity of pointer jumping.

The pointer jumping function takes as its input a directed layered
graph with a starting node and layers of nodes, and a single edge
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We consider the well known problem of determining the k'th
vertex reached by chasing pointers in a directed graph of
out-degree 1. The famous "pointer doubling" technique
provides an O(log k) parallel time algorithm on a
Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that ... more >>>

We consider the $k$-layer pointer jumping problem in the one-way
multi-party number-on-the-forehead communication model. In this problem,
the input is a layered directed graph with each vertex having outdegree
$1$, shared amongst $k$ players: Player~$i$ knows all layers {\em
except} the $i$th. The players must communicate, in the order
$1,2,\ldots,k$, ... more >>>

In this paper we study the one-way multi-party communication model,
in which every party speaks exactly once in its turn. For every
fixed $k$, we prove a tight lower bound of
$\Omega{n^{1/(k-1)}}$ on the probabilistic communication
complexity of pointer jumping in a $k$-layered tree, where the
pointers of the $i$-th ... more >>>