Optimal Congestion Control in Single Destination Networks

Stassinopoulos, G.I.; Konstantopoulos, Panagiotis

doi:10.1109/tcom.1985.1096380

Cited by 19 publications

(10 citation statements)

References 10 publications

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“…In this paper, we discuss a special case of dynamic network ow problems: we assume all transit times are zero. This special case has been considered in 2,9,15,19,14], among others. Dynamic network ow models with zero transit times capture some time-related issues: they can be used to model instances when network capacities restrict the quantity of ow that can be sent at any one time.…”

Section: Introductionmentioning

confidence: 99%

Faster Algorithms for the Quickest Transshipment Problem

Fleischer¹

2001

SIAM J. Optim.

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A transshipment problem with demands that exceed network capacity can be solved by sending ow in several waves. How can this be done in the minimum number of waves? This is the question tackled in the quickest transshipment problem. Hoppe and Tardos 10] describe the only known polynomial time algorithm to solve this problem. Their algorithm repeatedly minimizes submodular functions using the ellipsoid method, and is therefore not at all practical. We present an algorithm that nds a quickest transshipment with a polynomial number of maximum ow computations, and a faster algorithm that also uses minimum cost ow computations. When there is only one sink, we show how the algorithm can be sped up to return a solution using O(k) maximum ow computations, where k is the number of sources. Hajek and Ogier 9] describe an algorithm that nds a fractional solution to the singlesink quickest transshipment problem on a network with n nodes using O(n) maximum ow computations. They actually solve the universally quickest transshipment|a dynamic ow that minimizes the amount of supply left in the network at every moment of time. In this paper, we show how to solve this problem in O(mn log(n 2 =m)) time, the same asymptotic time required by the fastest known algorithm to compute a maximum ow.

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Section: Introductionmentioning

confidence: 99%

Faster Algorithms for the Quickest Transshipment Problem

Fleischer¹

2001

SIAM J. Optim.

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“…The reason such a transformation does not work here is because the arc capacities are upper bounds on the rate of flow per time period and do not correspond to the total amount of flow an arc may carry throughout an interval. Transshipment over time with zero transit times was discussed in [6,12,20,29]. Hajek and Ogier [12] described the first polynomial time algorithm to find a universally quickest transshipment when all transit times are instantaneous.…”

Section: Introductionmentioning

confidence: 99%

Universally maximum flow with piecewise‐constant capacities

Fleischer

2001

Networks

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A maximum flow over time generalizes standard maximum flow by introducing a time component. The object is to send as much flow from source to sink in T T T time units as possible, where capacities are interpreted as an upper bound on the rate of flow entering an arc. A related problem is the universally maximum flow, which is to send a flow from source to sink that maximizes the amount of flow arriving at the sink by time t t t simultaneously for all t t t ≤ ≤ ≤ T T T. We consider a further generalization of this problem that allows arc and node capacities to change over time. In particular, given a network with m m m arcs and n n n nodes, arc and node capacities that are piecewise constant functions of time with at most k k k breakpoints and a time bound T T T, we show how to compute a flow that maximizes the amount of flow reaching the sink in all time intervals (0,t t t] simultaneously for all 0 < < < t t t ≤ ≤ ≤ T T T,

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“…This special case has been considered in [2,5,6,12,15,22,14], among others. Flows over time with zero transit times capture some time-related issues: they can be used to model instances when network capacities restrict the quantity of flow that can be sent at any one time.…”

Section: Introductionmentioning

confidence: 99%

Optimal Rounding of Instantaneous Fractional Flows Over Time

Fleischer

Orlin

2000

SIAM J. Discrete Math.

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A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piece-wise linear convex functions of the flow? In this paper, we show that this problem can be solved using min{m,logT, l+og(mu)-g(U )} maximum flow computations and one minimum (convex) cost flow computation. Here m is the number of arcs, F is the maximum supply or demand, and U is the maximum capacity. When there is only one sink, this problem can be solved in the same asymptotic time as one minimum (convex) cost flow computation. This improves upon the recent algorithm in [5] which solves the quickest transshipment problem (the above mentioned problem without costs) on k terminals using k logT maximum flow computations and k minimum cost flow computations. Our solutions start with a stationary fractional flow, as described in [5], and use rounding to transform this into an integral flow. The rounding procedure takes O(n) time.

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Optimal Congestion Control in Single Destination Networks

Cited by 19 publications

References 10 publications

Faster Algorithms for the Quickest Transshipment Problem

Faster Algorithms for the Quickest Transshipment Problem

Universally maximum flow with piecewise‐constant capacities

Optimal Rounding of Instantaneous Fractional Flows Over Time

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