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• W50404825 abstract "We consider the problem of efficient distributed computation of arbitrary function on arbitrary communication network. The algorithm to compute the function is given by computation graph $mathcal{G}$ which is represented by weighted directed acyclic graph (DAG) and the communication network is represented by a weighted graph $mathcal{N}.$ We consider two variations of the problem. First we consider the problem of minimizing delay of computing the function. We prove that the problem is NP-hard when computation graph is a DAG and the communication network is arbitrary. We give an algorithm which solves this problem when the computation graph is tree structured in $O(pn^2)$ time where $p$ and $n$ are the number of vertices in $mathcal{G}$ and $mathcal{N},$ respectively. Then we looked at the problem of minimizing the cost of computing the function. We prove that this problem is also NP-hard for arbitrary computation and communication graph. There are many polynomial-time algorithms available in the literature when the computation graph is a tree. We give a polynomial-time algorithm when the computation graph is layered and takes $O(rn^{2k})$ where $r$ is the number of layers in $mathcal{G}$ and $k$ is the maximum number of vertices at any layer." @default.
• W50404825 created "2016-06-24" @default.
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• W50404825 date "2014-01-11" @default.
• W50404825 modified "2023-09-27" @default.
• W50404825 title "Efficient Embedding of Functions in Weighted Communication Networks." @default.
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