Priority-based distribution trees for application-level multicast

Vogel, Jürgen; Widmer, Joerg; Farin, Dirk; Mauve, Martin; Effelsberg, Wolfgang

doi:10.1145/963900.963914

Cited by 26 publications

(15 citation statements)

References 11 publications

(12 reference statements)

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“…Since then SLTs were shown to have numerous applications. In particular, they were found useful for various data gathering and dissemination tasks in overlay networks [14], [46], [37], in wireless and sensor networks [47], [21], [9], [44], and in the message-passing model of distributed computing [5], [6]. Other applications of SLTs include network and VLSIcircuit design [16], [17], [18], [43], and routing [48].…”

Section: For Every Vertex V ∈ V D T (Rt V) ≤ α · D G (Rt V) and mentioning

confidence: 99%

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

Elkin¹,

Solomon²

2015

SIAM J. Comput.

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Abstract-For a pair of parameters α, β ≥ 1, a spanning tree T of a weighted undirected n-vertex graph G = (V, E, w) is called an (α, β)-shallow-light tree (shortly, (α, β)-SLT) of G with respect to a designated vertex rt ∈ V if (1) it approximates all distances from rt to the other vertices up to a factor of α, and (2) its weight is at most β times the weight of the minimum spanning tree MST (G) of G. The parameter α (respectively, β) is called the root-distortion (resp., lightness) of the tree T . Shallowlight trees (SLTs) constitute a fundamental graph structure, with numerous theoretical and practical applications. In particular, they were used for constructing spanners, in network design, for VLSIcircuit design, for various data gathering and dissemination tasks in wireless and sensor networks, in overlay networks, and in the message-passing model of distributed computing.Tight tradeoffs between the parameters of SLTs were established by Awerbuch et al. [5], [6] and Khuller et al. [33]. They showed that for any > 0 there always exist (1 + , O( 1 ))-SLTs, and that the upper bound β = O( 1 ) on the lightness of SLTs cannot be improved. In this paper we show that using Steiner points one can build SLTs with logarithmic lightness, i.e., β = O(log 1 ). This establishes an exponential separation between spanning SLTs and Steiner ones.One particularly remarkable point on our tradeoff curve is = 0. In this regime our construction provides a shortest-path tree with weight at most O(log n) · w(MST (G)). Moreover, we prove matching lower bounds that show that all our results are tight up to constant factors.Finally, on our way to these results we settle (up to constant factors) a number of open questions that were raised by Khuller et al. [33] in SODA'93.

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Section: For Every Vertex V ∈ V D T (Rt V) ≤ α · D G (Rt V) and mentioning

confidence: 99%

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

Elkin¹,

Solomon²

2015

SIAM J. Comput.

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“…SLTs were found useful for numerous data gathering and dissemination tasks in overlay networks [10,44,34], in the message-passing model of distributed computing [5,6], and in wireless and sensor networks [45,9,18,36,35,43]. Moreover, SLTs find applications in routing [3,42,28,46] and in network and VLSI-circuit design [15,16,17,41].…”

Section: Journal Of Computational Geometry Jocgorgmentioning

confidence: 99%

Euclidean Steiner Shallow-Light Trees

Solomon

2014

Proceedings of the Thirtieth Annual Symposium on Computational Geometry

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Abstract. A spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree is called a shallow-light tree (shortly, SLT). More specifically, an (α, β)-SLT of a weighted undirected graph G = (V, E, w) with respect to a designated vertex rt ∈ V is a spanning tree of G with: (1) root-stretch α -it preserves all distances between rt and the other vertices up to a factor of α, and (2) lightness β -it has weight at most β times the weight of a minimum spanning tree M ST (G) of G. In this paper we show that Steiner points lead to a quadratic improvement in Euclidean SLTs, by presenting a construction of Euclidean Steiner (1 + , O( 1 ))-SLTs in arbitrary 2-dimensional Euclidean spaces. The lightness bound β = O( 1 ) of our construction is optimal up to a constant. The runtime of our construction, and thus the number of Steiner points used, are bounded by O(n).

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“…Constructing an efficient multicast tree under various constraints with regard to latency has been readily studied, e.g. [6,12,19,29]. None of these works, however, is directly applicable in our setting since instead of a single tree, we need to construct n partially overlapping multicast trees, one rooted at each node.…”

Section: Related Workmentioning

confidence: 99%

Maximizing total upload in latency-sensitive P2P applications

Douceur

Lorch

Moscibroda

2007

Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures

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Motivated by an application in distributed gaming, we define and study the latency-constrained total upload maximization problem. In this problem, a peer-to-peer overlay network is modeled as a complete graph and each node vi has an upload bandwidth capacity ci and a set of receivers R(i). Each sender-receiver pair (vi, vj ), where vj ∈ R(i), is a request that should be satisfied, i.e., vi should send a data packet to each vj ∈ R(i). The goal is to find a set of at most n multicast-trees Ti of depth at most 2, such that each node can be part of multiple trees, all capacity constraints are met, and the number of satisfied requests is maximized. In this paper, we prove that the problem is NP-complete, and we present an algorithm with approximation ratio 1 − 2/ √ cmin, where cmin is the minimum upload capacity. Finally, we also study the impact of network coding on the quality and approximability of the solution.

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Priority-based distribution trees for application-level multicast

Cited by 26 publications

References 11 publications

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

Steiner Shallow-Light Trees Are Exponentially Lighter than Spanning Ones

Euclidean Steiner Shallow-Light Trees

Maximizing total upload in latency-sensitive P2P applications

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