On the Maximum Rate of Networked Computation in a Capacitated Network - 2017


We tend to are given a capacitated Communication network and many infinite sequences of source knowledge each of which is out there at some node within the network. A operate of the source information is to be computed in the network and made accessible at a sink node that is additionally on the network. The schema to compute the perform is given as a directed acyclic graph (DAG). We tend to need to get a computation and Communication schedule within the network to maximise the speed of computation of the operate for an arbitrary operate (represented by DAG). We tend to initial analyze the complexity of finding the speed maximizing schedule for the final DAG. We show that finding an optimal schedule is such as solving a packing linear program (LP). We have a tendency to then prove that finding the most rate is MAX SNP-exhausting (by analyzing this packing LP) even when the DAG has bounded degree, bounded edge weights and therefore the network has three vertices. We tend to then consider special cases arising in sensible situations. 1st, a polynomial time algorithm for the network with 2 vertices is presented. This algorithm may be a reduction to a version of a submodular operate minimization downside. Next, for the final network we describe a restricted class of schedules and its equivalent packing LP. By relating this LP to minimum value embedding downside, we present approximation algorithms for special classes of DAGs.

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