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Abstract:
Many applications in parallel processing have to traverse large,
implicitly defined trees with irregular shape. The receiver initiated
load balancing algorithm \emph{random polling} has long been known to
be very efficient for these problems in practice. For any
$\epsilon>0$, we prove that its parallel execution time is at most
$(1+\epsilon)\Tseq/\proc + \Oh{\Tatomic + h(\frac{1}{\epsilon} +
\Trouting + \Tsplit)}$ with high probability, where $\Trouting$,
$\Tsplit$ and $\Tatomic$ bound the time for sending a message,
splitting a subproblem and finishing a small unsplittable subproblem
respectively. The \emph{maximum splitting depth} $h$ is related to the
depth of the computation tree. Previous work did not prove efficiency
close to one and used less accurate models. In particular, our machine
model allows asynchronous communication with nonconstant message
delays and does not assume that communication takes place in
rounds. This model is compatible with the LogP model.
