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621
Multicommodity flow
, 2005
"... Leighton and Rao use multicommodity flow results to design the first polynomial time approximation algorithms for well known NP-Hard optimization problems. Such problems include graph ..."
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Leighton and Rao use multicommodity flow results to design the first polynomial time approximation algorithms for well known NP-Hard optimization problems. Such problems include graph
Multicommodity Flows
"... In this lecture, we consider multicommodity flow problems and the relationships between maximum flows and minimum cuts in such networks. It is well-known that for a single commodity, the max-flow is equal to the min-cut; however, this does not generalize for multiple commodities. Here, we will discu ..."
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In this lecture, we consider multicommodity flow problems and the relationships between maximum flows and minimum cuts in such networks. It is well-known that for a single commodity, the max-flow is equal to the min-cut; however, this does not generalize for multiple commodities. Here, we
Multicommodity Flows and Column Generation
, 2006
"... The goal of this chapter is to give a short introduction into multicommodity flows and column generation. Both will be used later on. ..."
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The goal of this chapter is to give a short introduction into multicommodity flows and column generation. Both will be used later on.
MULTICOMMODITY FLOW PROBLEMS
"... Solving large scale linear multicommodity flow problems with an active set strategy and proximal-accpm ..."
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Solving large scale linear multicommodity flow problems with an active set strategy and proximal-accpm
Multicommodity Flows and Approximation Algorithms
, 1994
"... This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a ground-breaking work Leighton and Rao [34] showed an approximate max-flow min-cut theorem for uniform multicommodity flow and used this to obtain an approximation ..."
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Cited by 5 (0 self)
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This thesis is about multicommodity flows and their use in designing approximation algorithms for problems involving cuts in graphs. In a ground-breaking work Leighton and Rao [34] showed an approximate max-flow min-cut theorem for uniform multicommodity flow and used this to obtain
Multicommodity flow in Polynomial time
, 2009
"... The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising polynomial time solvability of the problem in two broad situations ..."
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The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising polynomial time solvability of the problem in two broad
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 LP-based approximation algorithm The integer multicommodity flow problem can be written
Faster and simpler algorithms for multicommodity flow and other fractional packing problems
"... This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We present new faster and much simpler algorithms for these problems. ..."
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Cited by 325 (5 self)
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This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We present new faster and much simpler algorithms for these problems.
Criticality for multicommodity flows
- J. Combinatorial Theory, Ser. B
"... Abstract For k ≥ 1, the k-commodity flow problem is, we are given k pairs of vertices in a graph G, and we ask whether there exist k flows in the graph, where • the ith flow is between the ith pair of vertices, and has total value one; and • for each edge e, the sum of absolute values of the flows ..."
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Cited by 36 (1 self)
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in which all flow values are multiples of 1/p, and • a very simple polynomial-time algorithm to solve the (k, p) multicommodity flow problem when p > 1.
On the Core of the Multicommodity Flow Game
"... In [26], Papadimitriou proposed a game theoretic framework for analyzing incentive issues in Internet routing. In particular he defined the following coalitional game: Given a network with a multicommodity flow satisfying node capacity and demand constraints, the payoff of a node is the total flow o ..."
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In [26], Papadimitriou proposed a game theoretic framework for analyzing incentive issues in Internet routing. In particular he defined the following coalitional game: Given a network with a multicommodity flow satisfying node capacity and demand constraints, the payoff of a node is the total flow
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621
