Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
Complexity classification of network information flow problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Combinatorica
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
Information flow decomposition for network coding
IEEE Transactions on Information Theory
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The non-uniform demand network coding problem is posed as a single-source and multiple-sink network transmission problem where the sinks may have heterogeneous demands. In contrast with multicast problems, non-uniform demand problems are concerned with the amounts of data received by each sink, rather than the specifics of the received data. In this work, we enumerate non-uniform network demand scenarios under which network coding solutions can be found in polynomial time. This is accomplished by relating the demand problem with the graph coloring problem, and then applying results from the strong perfect graph theorem to identify coloring problems which can be solved in polynomial time. This characterization of efficiently-solvable non-uniform demand problems is an important step in understanding such problems, as it allows us to better understand situations under which the NP-complete problem might be tractable.