Packing algorithms for arborescences (and spanning trees) in capacitated graphs

Gabow, Harold N.; Manu, K. S.

doi:10.1007/3-540-59408-6_67

Cited by 13 publications

(18 citation statements)

References 13 publications

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“…In [9] it was shown that this is a tight bound. [12] established an efficient optimal solution to the tree packing problem for directed capacitated graphs.…”

Section: Efficient Optimal Solution To the Multi-topology Problemmentioning

confidence: 99%

Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas

Orda

Yassour

2005

Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing

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A major problem in wireless networks is how to route either broadcast, unicast or multicast traffic so as to maximize the lifetime, i.e., the time until the battery of a transmitting node drains out. Focusing on the fundamental single-session problem, our solution approach is based on the employment of multi-topology routing schemes. Such a scheme consists of a set of routing topologies, which are employed sequentially, for some prescribed duration times.First, we consider the standard wireless environment of multiple recipients, which correspond to omnidirectional antennas. For the cases of either single-topology schemes or unicast sessions, we establish optimal solutions of polynomial complexity. For the general (multi-topology) cases of broadcast and multicast, which are NP-hard, we derive a novel heuristic scheme, and demonstrate its efficiency by way of simulations.We then consider an alternative, single-recipient wireless environment, which corresponds to the important case of directional antennas. While the employment of directional antennas is known to posses significant advantages over the traditional omnidirectional transmission, the problem of lifetime maximization under this environment has received only limited attention. We demonstrate that the change from the traditional (multiple-recipients) environment to the singlerecipient environment is of major significance in terms of computational complexity and produces an interesting twist of difficulty: namely, for the standard model, the singletopology broadcast problem is computationally solvable and the multi-topology problem is NP-hard, while the opposite holds for the single-recipient model. Finally, we discuss the extension of our results to the case of multiple sessions.

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“…In [9] it was shown that this is a tight bound. [12] established an efficient optimal solution to the tree packing problem for directed capacitated graphs.…”

Section: Efficient Optimal Solution To the Multi-topology Problemmentioning

confidence: 99%

Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas

Orda

Yassour

2005

Proceedings of the 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing

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“…When edges have capacities, this problem has been well-studied since the 1970s -Edmonds, Lovasz and Gabow and others have given centralized schemes based on packing spanning trees [1]- [5].…”

Section: Introductionmentioning

confidence: 99%

“…INTRODUCTION We consider the problem of broadcasting a live stream of data, such as a movie, to all nodes in an unstructured network. When edges have capacities, this problem has been well-studied since the 1970s -Edmonds, Lovasz and Gabow and others have given centralized schemes based on packing spanning trees [1]- [5].…”

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confidence: 99%

Randomized Decentralized Broadcasting Algorithms

Massoulié

Twigg

Gkantsidis

et al. 2007

IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications

154

182

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We consider the problem of broadcasting a live stream of data in an unstructured network. The broadcasting problem has been studied extensively for edge-capacitated networks. We give the first proof that whenever demand λ + ε is feasible for ε > 0, a simple local-control algorithm is stable under demand λ, and as a corollary a famous theorem of Edmonds. We then study the node-capacitated case and show a similar optimality result for the complete graph. We study through simulation the delay that users must wait in order to playback a video stream with a small number of skipped packets, and discuss the suitability of our algorithms for live video streaming. I. INTRODUCTIONWe consider the problem of broadcasting a live stream of data, such as a movie, to all nodes in an unstructured network. When edges have capacities, this problem has been well-studied since the 1970s -Edmonds, Lovasz and Gabow and others have given centralized schemes based on packing spanning trees [1]- [5].The broadcast problem is at the core of every content distribution system; in particular, current live streaming distribution systems such as CoolStreaming [6], PPLive [7], SplitStream [8]. These systems either construct the overlay topology in such a way to easy packet scheduling, and in doing so reduce the network efficiency by not optimally using all the available resources, or use heuristic algorithms for packet distribution with unknown performance properties.We present a completely distributed and suprisingly simple algorithm for broadcasting in arbitrary networks, which does not require coding yet provably achieves the optimal broadcast rate. This is the first known result of this kind. Our analysis is based on fluid models and Lyapunov functions applied to a novel powerset representation of the network. As a corollary we retrieve a famous theorem of Edmonds [1].In the second part of the paper, we introduce a new model for broadcasting a live stream of data in a peer-to-peer network based on the node-capacitated broadcast problem -each node has a specified upload capacity (we assume that download capacity is infinite), modeling the user's connection to the network, and the user must choose how this capacity is allocated among peers. This introduces an allocation problem in addition to the problem of scheduling packet transmissions. We present a completely distributed algorithm for the nodecapacitated broadcast problem, and show that it achieves the optimal rate in certain classes of network.

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“…Our scheme finds an optimal packing using at most n edges with positive multiplicities, performing minimization for the clutter at most n times and minimization for its blocker at most n 2 times, where n denotes the cardinality of the vertex set. The scheme can be regarded as generalization of an algorithm for fractional packing of r -arborescences proposed by Gabow and Manu [8], and an algorithm for fractional packing of T -joins given by Barahona [1].…”

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confidence: 99%

Fractional packing in ideal clutters

Matsuoka

2010

Math. Program.

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This paper presents a generic scheme for fractional packing in ideal clutters. Consider an ideal clutter with a nonnegative capacity function on its vertices. It follows from ideality that for any nonnegative capacity the total multiplicity of an optimal fractional packing is equal to the minimum capacity of a vertex cover. Our scheme finds an optimal packing using at most n edges with positive multiplicities, performing minimization for the clutter at most n times and minimization for its blocker at most n 2 times, where n denotes the cardinality of the vertex set. Applied to the clutter of dijoins (directed cut covers), the scheme provides the first combinatorial polynomial-time algorithm for fractional packing of dijoins.

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Packing algorithms for arborescences (and spanning trees) in capacitated graphs

Cited by 13 publications

References 13 publications

Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas

Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas

Randomized Decentralized Broadcasting Algorithms

Fractional packing in ideal clutters

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