1 research outputs found
Scalar Solvability of Network Computation Problems and Representable Matroids
We consider the following \textit{network computation problem}. In an acyclic
network, there are multiple source nodes, each generating multiple messages,
and there are multiple sink nodes, each demanding a function of the source
messages. The network coding problem corresponds to the case in which every
demand function is equal to some source message, i.e., each sink demands some
source message. Connections between network coding problems and matroids have
been well studied. In this work, we establish a relation between network
computation problems and representable matroids. We show that a network
computation problem in which the sinks demand linear functions of source
messages admits a scalar linear solution if and only if it is matroidal with
respect to a representable matroid whose representation fulfills certain
constraints dictated by the network computation problem. Next, we obtain a
connection between network computation problems and functional dependency
relations (FD-relations) and show that FD-relations can be used to characterize
network computation problem with arbitrary (not necessarily linear) function
demands as well as nonlinear network codes.Comment: 7 pages, 2 figures and 1 table. arXiv admin note: text overlap with
arXiv:1603.0536