Introduction to Algorithms
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
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Network coding theory: single sources
Communications and Information Theory
Foundations and Trends® in Networking
On the tradeoffs of implementing randomized network coding in multicast networks
IEEE Transactions on Communications
Worst-case optimal join algorithms: [extended abstract]
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
ℓ2/ℓ2-Foreach sparse recovery with low risk
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider the general network information flow problem, which was introduced by Ahlswede et. al[1]. We show a periodicity effect: for every integer m ≥ 2, there exists an instance of the network information ow problem that admits a solution if and only if the alphabet size is a perfect mth power. Building on this result, we construct an instance with O(m) messages and O(m) nodes that admits a solution if and only if the alphabet size is an enormous 2exp(Ω(m1/3)). In other words, if we regard each message as a length-k bit string, then k must be exponential in the size of the network. For this same instance, we show that if edge capacities are slightly increased, then there is a solution with a modest alphabet size of O(2m). In light of these results, we suggest that a more appropriate model would assume that the network operates at slightly under capacity.