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Short proofs on multicommodity flows and cuts
1991
Journal of combinatorial theory. Series B (Print)
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However, this contradicts the fact that Iw-)I = M-w I As is well known, this corollary implies a half-integral multicommodity flow theorem of Lomonosov [7] (extending the max-flow min-cut theorem of Ford ...
As was noted by Karzanov [4] and Seymour 1143, cut packing results (like Karzanov's theorem above) can be interpreted in terms of polyhedral cones, and thus by polarity of cones are related to multicommodity ...
doi:10.1016/0095-8956(91)90052-l
fatcat:biiskzq6affwrbvt3sbipwnlrm
Hallucination Helps: Energy Efficient Virtual Circuit Routing
[chapter]
2013
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
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The analysis of the online algorithm introduces a natural "priority" multicommodity flow problem, and bounds the priority multicommodity flow-cut gapthis might also be of independent interest. ...
The analysis of the approximation ratio is then a direct consequence of the flow-cut gap for multicommodity flow. ...
between concurrent multicommodity flow and sparsest cut [25, 26] ). ...
doi:10.1137/1.9781611973402.84
dblp:conf/soda/AntoniadisIKMNPS14
fatcat:ex2aqsgkjvgk3jdcamit4usor4
Edge-Disjoint Paths in Planar Graphs with Constant Congestion
2009
SIAM journal on computing (Print)
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The natural multicommodity flow relaxation has an Ω( √ n) integrality gap where n is the number of nodes in G. ...
Another ingredient we develop is a constant factor approximation for the all-or-nothing flow problem on OS instances via the flow relaxation. ...
Chandra Chekuri and F. Bruce Shepherd acknowledge support from an ONR basic research grant N00014-05-1-0256 to Bell Labs. ...
doi:10.1137/060674442
fatcat:dcamyxlpyfanro6hkpisxtus7i
Edge-disjoint paths in Planar graphs with constant congestion
2006
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06
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The natural multicommodity flow relaxation has an Ω( √ n) integrality gap where n is the number of nodes in G. ...
Another ingredient we develop is a constant factor approximation for the all-or-nothing flow problem on OS instances via the flow relaxation. ...
Chandra Chekuri and F. Bruce Shepherd acknowledge support from an ONR basic research grant N00014-05-1-0256 to Bell Labs. ...
doi:10.1145/1132516.1132621
dblp:conf/stoc/ChekuriKS06
fatcat:o7cdx42fdzhxnnq7vnh5hfucma
A New Algorithm for Multicommodity Flow
[article]
2010
arXiv
pre-print
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We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. ...
A record is made of these cuts and the paths flowing through the edges of these cuts. This record is then utilized to develop our algorithm to obtain max flow for multicommodity flow. ...
Proof: The algorithm begins with applying max flow min cut theorem individually and separately to each source/sink pair of the given multicommodity flow and produces separate record of paths, min cuts, ...
arXiv:1001.0629v2
fatcat:yzkzashikfgm5egg66akw4heii
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
1999
Journal of the ACM
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In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. ...
In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. ...
ACKNOWLEDGMENTS The proof of Theorem 7 was suggested by Eva Tardos. The fact that Theorem 2 could be extended in this way was also pointed out by David Shmoys and Alistair Sinclair. ...
doi:10.1145/331524.331526
fatcat:ec6h6h56brgn3hdcln3kkzoshy
Short length menger's theorem and reliable optical routing
2003
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03
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In fact, this is only a corollary of a stronger result for multicommodity flow on networks with unit edge capacities: any multicommodity flow with k units for each commodity can be rerouted such that the ...
We propose an O(k 2 F ) = O(k 2 −1 log n) approximation algorithm for this problem where F is the flow number of the graph, is the maximum degree and is the expansion. ...
Acknowledgements We would like to thank Ankur Bhargava and Christian Scheideler for many useful discussions, and the anonymous referees for their helpful suggestions. ...
doi:10.1145/777449.777453
fatcat:kk2e7g7elbfjvfydl2xovqeu7q
Short length Menger's theorem and reliable optical routing
2005
Theoretical Computer Science
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In fact, this is only a corollary of a stronger result for multicommodity flow on networks with unit edge capacities: any multicommodity flow with k units for each commodity can be rerouted such that the ...
We propose an O(k 2 F ) = O(k 2 −1 log n) approximation algorithm for this problem where F is the flow number of the graph, is the maximum degree and is the expansion. ...
Acknowledgements We would like to thank Ankur Bhargava and Christian Scheideler for many useful discussions, and the anonymous referees for their helpful suggestions. ...
doi:10.1016/j.tcs.2005.03.009
fatcat:wyd6f6qadjh4bic2isge7oaxde
Short length menger's theorem and reliable optical routing
2003
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03
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In fact, this is only a corollary of a stronger result for multicommodity flow on networks with unit edge capacities: any multicommodity flow with k units for each commodity can be rerouted such that the ...
We propose an O(k 2 F ) = O(k 2 −1 log n) approximation algorithm for this problem where F is the flow number of the graph, is the maximum degree and is the expansion. ...
Acknowledgements We would like to thank Ankur Bhargava and Christian Scheideler for many useful discussions, and the anonymous referees for their helpful suggestions. ...
doi:10.1145/777412.777453
dblp:conf/spaa/BagchiCK03
fatcat:cooermxbmvhlrhhkw626prbx7q
An approximate max-flow min-cut relation for undirected multicommodity flow, with applications
1995
Combinatorica
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In this paper, we prove the first approximate max-flow min-cut theorem for undirected multicommodity flow. ...
and D is the sum of demands. ...
We gratefully acknowledge helpful conversations with Tom Leighton, John Reif, David Shmoys, and ]~va Tardos.
AN APPROXIMATE MAX-FLOW MIN-CUT THEOREM ...
doi:10.1007/bf01200755
fatcat:sdvzwb7w4nh47ioreboijkhg74
Multicommodity Flows in Planar Graphs with Demands on Faces
[article]
2020
arXiv
pre-print
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We consider the problem of multicommodity flows in planar graphs. Seymour showed that if the union of supply and demand graphs is planar, then the cut condition is sufficient for routing demands. ...
We show that if the source sink pairs on each face of the graph are such that sources and sinks appear contiguously on the cycle bounding the face, then the flow cut gap is at most 3. ...
Theorem 4 Let (G, H) be a separable face instance of multicommodity flow . Then, the flow-cut gap of (G, H) is at most 3. Proof. Follows from Lemma 2 and Theorem 3. Proof. ...
arXiv:2007.01280v1
fatcat:gm4nr6njajbilpcobn56rpxz34
Extensions and limits to vertex sparsification
2010
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
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Indirectly our result also allows us to give a construction for better quality cut sparsifiers (and flow sparsifiers). ...
bounds against many multicommodity flows at once. ...
on only short paths, using local paths. ...
doi:10.1145/1806689.1806698
dblp:conf/stoc/LeightonM10
fatcat:oniwcypynfdhhnmsegsug5fbqm
Page 572 of Mathematical Reviews Vol. 31, Issue 3
[page]
1966
Mathematical Reviews
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The main result is a generalization of the max-flow, min-cut theorem for multicommodity flows in bi-path networks. ...
Bi-path networks and multicommodity flows. IEEE Trans. Cirewit Theory CT-11 (1964), 468-474. ...
Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
2013
Theory of Computing Systems
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Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity flows and cuts. ...
The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and flows, for h ≤ 3: The size of a minimum h-route cut is at least f /h and at most O(log 3 k ·f ) where ...
The first author would like to thank Jiří Sgall and Thomas Erlebach for stimulating discussions. ...
doi:10.1007/s00224-013-9454-3
fatcat:vjlestmhavezhmuumfcb5bw6uy
Improving the multicommodity flow rates with network codes for two sources
2009
IEEE Journal on Selected Areas in Communications
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The scheme we suggest is based on modifying the multicommodity flow solution and thus improving the achievable rate region, w.r.t the uncoded case. ...
For both the nondistributed case and the distributed case, the computational complexity of our algorithm for network coding is comparable to that of the parallel multicommodity flow problem. ...
Improving the Multicommodity Flow Suppose we are given a rate pair (R 1 , R 2 ), which is on the boundary of the rate region of the multicommodity flow. ...
doi:10.1109/jsac.2009.090620
fatcat:izgyodngkfcrzaviykuprpe7na
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