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MULTICOMMODITY FLOW PROBLEMS
"... Solving large scale linear multicommodity flow problems with an active set strategy and proximalaccpm ..."
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Solving large scale linear multicommodity flow problems with an active set strategy and proximalaccpm
The Integer Multicommodity Flow Problem
"... + (v) are the sets of arcs into and out of v, respectively. 3. demand: P e2ffi + (s i ) f i (e) d i . 4. integrality: all the flows f i (e) are integral. As stated above, the problem may be infeasible if the capacities available do not suffice to satisfy the demands. This lecture considers the ..."
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the integer multicommodity flow problem where we do not enforce any demand constraints, the flow shipped for any commodity is less or equal to 1, and the goal is to maximize the total flow over all commodities. 2 An LPbased approximation algorithm The integer multicommodity flow problem can be written
The Quickest Multicommodity Flow Problem
 INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 2002
"... Traditionally, ows over time are solved in timeexpanded networks which contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static ows, its main and often fatal drawback is the enormous size of the tim ..."
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Cited by 34 (11 self)
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Traditionally, ows over time are solved in timeexpanded networks which contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static ows, its main and often fatal drawback is the enormous size of the timeexpanded network. In particular, this approach usually does not lead to efficient algorithms with running time polynomial in the input size since the size of the timeexpanded network is only pseudopolynomial. We present two
Fast Approximation Algorithms for Multicommodity Flow Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1991
"... All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms [15] uses a fast matrix multiplication algorithm and takes O(k 3:5 n 3 m :5 log(nDU )) time for the multicommodity flow problem with inte ..."
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Cited by 191 (21 self)
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All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms [15] uses a fast matrix multiplication algorithm and takes O(k 3:5 n 3 m :5 log(nDU )) time for the multicommodity flow problem
A Survey of Algorithms for Convex Multicommodity Flow Problems
, 1997
"... There are many problems related to the design of networks. Among them, the message routing problem plays a determinant role in the optimization of network performance. Much of the motivation for this work comes from this problem which is shown to belong to the class of nonlinear convex multicommodit ..."
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Cited by 30 (4 self)
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multicommodity flow problems. This paper emphasizes the message routing problem in data networks, but it includes a broader literature overview of convex multicommodity flow problems. We present and discuss the main solution techniques proposed for solving this class of largescale convex optimization problems
A Simple Method for . . . for the Multicommodity Flow Problem
, 2005
"... We present a new efficient approach for solving the multicommodity flow problem as a sequence of subproblems, each on a very sparse but connected network. We show that each subproblem can be contracted to a problem on a much smaller graph. We then solve these problems using the simplex method. We te ..."
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We present a new efficient approach for solving the multicommodity flow problem as a sequence of subproblems, each on a very sparse but connected network. We show that each subproblem can be contracted to a problem on a much smaller graph. We then solve these problems using the simplex method. We
On an Integer Multicommodity Flow Problem from the Airplane Industry
, 1997
"... Here we discuss a new integer multicommodity flow problem in which the commodities can not be shipped independently. The problem emerges in the routing of airplane parts from production sites to assembly sites. The parts are of such size that they have to be carried on dedicated trailers. Each type ..."
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Cited by 2 (0 self)
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Here we discuss a new integer multicommodity flow problem in which the commodities can not be shipped independently. The problem emerges in the routing of airplane parts from production sites to assembly sites. The parts are of such size that they have to be carried on dedicated trailers. Each type
Interior Point Methods for Linear Multicommodity Flow Problems
"... Abstract This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primaldual interiorpoint method is designed to solve the problem. In the interiorpoint method, at each iteration, the corresp ..."
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Abstract This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primaldual interiorpoint method is designed to solve the problem. In the interiorpoint method, at each iteration
Faster Approximation Schemes for Fractional Multicommodity Flow Problems
"... We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of minimum possible dependency on the number of commodities k. We showthat by modifying the algorithms by Garg & K"onemann [7] and Fleischer [5] we can reduce their running ..."
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Cited by 29 (0 self)
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We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of minimum possible dependency on the number of commodities k. We showthat by modifying the algorithms by Garg & K"onemann [7] and Fleischer [5] we can reduce their running
Results 1  10
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