2006
DOI: 10.1109/tit.2005.864474
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Network routing capacity

Abstract: Abstract-We define the routing capacity of a network to be the supremum of all possible fractional message throughputs achievable by routing. We prove that the routing capacity of every network is achievable and rational, we present an algorithm for its computation, and we prove that every non-negative rational number is the routing capacity of some network. We also determine the routing capacity for various example networks. Finally, we discuss the extension of routing capacity to fractional coding solutions … Show more

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Cited by 78 publications
(118 citation statements)
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“…where γ t,i is defined in (2). By choosing the real coefficients α e→e ′ and β t,i , the goal is to minimize F .…”
Section: T)mentioning
confidence: 99%
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“…where γ t,i is defined in (2). By choosing the real coefficients α e→e ′ and β t,i , the goal is to minimize F .…”
Section: T)mentioning
confidence: 99%
“…We can apply the quasi-linear network-coding scheme to this network, and since the two sub-networks operate separately, get a solution with rate 7/20 > 1/3. We can compare this with the best routing solution for this network which has a lower rate of 1/3 (see [2]). …”
Section: Theoremmentioning
confidence: 99%
“…However, more guarantees can be obtained once we operate a subset of the sinks below their best-case capacity (d i < c i ). This concept of achieving more by relaxing the strict capacity requirement has already appeared in the network coding literature, and was found significantly useful [7], [8]. Here the idea is that with three or more partial demand sinks, for some sink we may exhaust the ways of zeroing columns using non-contaminating column operations.…”
Section: B More Than Two Partial Demand Sinksmentioning
confidence: 99%
“…Vector network coding as part of fractional network coding was mentioned in [2]. A solution of the network is called an (s, t) fractional vector network coding solution, if the edges transmit vectors of length t, but the message vectors are of length s ≤ t. The case s = t = 1 corresponds to a scalar solution.…”
Section: Introductionmentioning
confidence: 99%