Local phy + global flow: A layering principle for wireless networks

Kannan, Sreeram; Raja, A.; Viswanath, Pramod

doi:10.1109/isit.2011.6033821

Cited by 16 publications

(16 citation statements)

References 16 publications

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“…We also consider the notion of undirected polymatroidal networks and observe that they provide a natural way to generalize flows and cuts in edge and node capacitated undirected networks.We establish poly-logarithmic flow-cut gap results in several scenarios that have been previously considered in the standard network flow models where capacities are on the edges or nodes [25,26,14,23,13]. Our results from a preliminary version have already found applications in wireless network information flow [20,21] and we anticipate more in the future. On the technical side our key tools are the formulation and analysis of the dual of the flow relaxations via continuous extensions of submodular functions, in particular the Lovász extension.…”

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confidence: 69%

Multicommodity Flows and Cuts in Polymatroidal Networks

Chekuri¹,

Kannan²,

Raja³

et al. 2015

SIAM J. Comput.

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We consider multicommodity flow and cut problems in polymatroidal networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel [24] and Hassin [18] in the single-commodity setting and are closely related to the submodular flow model of Edmonds and Giles [10]; the well-known maxflow-mincut theorem holds in this more general setting. Polymatroidal networks for the multicommodity case have not, as far as the authors are aware, been previously explored. Our work is primarily motivated by applications to information flow in wireless networks. We also consider the notion of undirected polymatroidal networks and observe that they provide a natural way to generalize flows and cuts in edge and node capacitated undirected networks.We establish poly-logarithmic flow-cut gap results in several scenarios that have been previously considered in the standard network flow models where capacities are on the edges or nodes [25,26,14,23,13]. Our results from a preliminary version have already found applications in wireless network information flow [20,21] and we anticipate more in the future. On the technical side our key tools are the formulation and analysis of the dual of the flow relaxations via continuous extensions of submodular functions, in particular the Lovász extension. For directed graphs we rely on a simple yet useful reduction from polymatroidal networks to standard networks. For undirected graphs we rely on the interplay between the Lovász extension of a submodular function and line embeddings with low average distortion introduced by Matousek and Rabinovich [29]; this connection is inspired by, and generalizes, the work of Feige, Hajiaghayi and Lee [13] on node-capacitated multicommodity flows and cuts. The applicability of embeddings to flow-cut gaps in polymatroidal networks is of independent mathematical interest.

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confidence: 69%

Multicommodity Flows and Cuts in Polymatroidal Networks

Chekuri¹,

Kannan²,

Raja³

et al. 2015

SIAM J. Comput.

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“…By identifying a directed acyclic subnetwork that is sufficient to approximately maintain capacity, our result can be used to reduce the delay and complexity of such schemes by suggesting links that could be potentially shut down. Although shutting down individual links in wireless networks may be nontrivial since these links may represent overheard transmissions over other links, certain networks such as Gaussian networks consisting of isolated links or only MAC and broadcast components (as studied in [11] and [22]) provide some freedom in controlling individual links. Indeed, simplification can be possible even in more general networks.…”

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confidence: 99%

On Feedback in Gaussian Multihop Networks

Chern

Farnia

Özgür

2015

IEEE Trans. Inform. Theory

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The study of feedback has been mostly limited to single-hop communication settings. In this paper, we consider Gaussian networks where sources and destinations can communicate with the help of intermediate relays over multiple hops. We assume that links in the network can be bidirected providing opportunities for feedback. We ask the following question: can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rates in the network? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? We show that in any arbitrary Gaussian network with bidirected edges and cycles and unicast traffic, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. For Gaussian networks with multiple-access and broadcast traffic, an acyclic subnetwork is sufficient to achieve every rate point in the capacity region of the original network, however, there may not be a single acyclic subnetwork that maintains the whole capacity region. For networks with multicast and multiple unicast traffic, on the other hand, bidirected information flow across certain links can be critically needed to maximize the end-to-end capacity region. These results can be regarded as generalizations of the conclusions regarding the usefulness of feedback in various single-hop Gaussian settings and can provide opportunities for simplifying operation in Gaussian multihop networks.

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“…5.1.3) still has a flow-cut gap of one. Polymatroidal flows are equivalent to submodular flows, and have recently gained attention for modeling information flow in wireless networks [13,41,42]. Their dual problem is a minimum cut problem where the edge weights are defined by a convolution of local submodular functions [54].…”

Section: Relation To the Literaturementioning

confidence: 99%

Graph cuts with interacting edge weights: examples, approximations, and algorithms

Jegelka

Bilmes

2016

Math. Program.

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We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and computer vision. In this paper, we connect these applications via the generic formulation of "cooperative graph cuts", for which we study complexity, algorithms, and connections to polymatroidal network flows. Finally, we compare the proposed algorithms empirically.

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Local phy + global flow: A layering principle for wireless networks

Cited by 16 publications

References 16 publications

Multicommodity Flows and Cuts in Polymatroidal Networks

Multicommodity Flows and Cuts in Polymatroidal Networks

On Feedback in Gaussian Multihop Networks

Graph cuts with interacting edge weights: examples, approximations, and algorithms

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