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- W4226271765 abstract "One of the important unsolved problems in information theory is the conjecture that the undirected multiple-unicast network information capacity is the same as the routing capacity. This conjecture is verified only for a handful of networks and network classes. Moreover, only two explicit upper bounds on information capacity are known for general undirected networks: the sparsest cut bound and the linear programming bound. In this paper, we present an information-theoretic upper bound, called the <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>partition bound</i> , on the capacity of general undirected multiple-unicast networks. We show that a decision version problem of computing the bound is NP-complete. We present two classes of undirected multiple-unicast networks such that the partition bound is achievable by routing. Thus, the conjecture is proved for these classes of networks. Recently, the conjecture was proved for a new class of networks defined by properties relating to cut-set and source-sink paths. We show the existence of a network outside of this new class of networks such that the partition bound is achievable by routing." @default.
- W4226271765 created "2022-05-05" @default.
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- W4226271765 date "2022-07-01" @default.
- W4226271765 modified "2023-10-14" @default.
- W4226271765 title "A Bound on Undirected Multiple-Unicast Network Information Flow" @default.
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- W4226271765 doi "https://doi.org/10.1109/tit.2022.3157623" @default.
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