## Spanners and Message Distribution in Networks (1999)

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Citations: | 6 - 0 self |

### BibTeX

@MISC{Farley99spannersand,

author = {Arthur M. Farley and Andrzej Proskurowski and Daniel Zappala and Kurt Windisch and Kurt},

title = {Spanners and Message Distribution in Networks},

year = {1999}

}

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### Abstract

. We investigate the applicability of spanners as shared structures that offer both low cost and low delay for broadcast and multicast. A k-spanner has the potential to offer lower delay than shared trees because it limits the distance between any two nodes in the network to a multiplicative factor k of the shortest-path distance. Using simulation over random topologies, we compare k-spanners to single-source minimum-distance spanning trees and show that a k-spanner can have similar cost and lower delay. We illustrate that by varying the value of k a spanner can be made to gradually favor cost over delay. These results indicate that it is feasible to build a multicast routing protocol using spanners as a shared communication structure. 1 Introduction Current multicast routing protocols can be classified as constructing either a separate shortest path tree for each sender to a group or a single shared tree for all senders. The tradeoffs between these two approaches have been...

### Citations

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- 1988
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Citation Context ... preference scheme has the probability decreasing exponentially with the distance between the two vertices on the plane ([Zegura et al. 1996]). The locality method we used is the basic Waxman model, [=-=Waxman 1988-=-] in which the probability of an edge being added between two vertices is ffe \Gammad=(fiL) where d is the distance between the vertices on the plane and ff and fi are parameters of the method. An inc... |

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Citation Context ...t we have conducted to provide some answers to these questions. There are a number of multicast protocols under consideration for use in administrative domains on the Internet [Ballardie et al. 1993; =-=Deering et al. 1996-=-]. All rely upon establishing a distribution tree that covers the receivers of a multicast group. There are two primary ways for characterizing trees used by the protocols. In a protocol using sender-... |

424 | Distance Vector Multicast Routing Protocol
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- 1988
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Citation Context ...e tractable than algorithms for stanners (where only a subset of nodes are members). Broadcast is also the basis for bootstrapping multicast communication in several multicast protocols, namely DVMRP =-=[12]-=- and PIM [7]. Both of these protocols build a separate shortest-path tree for each sender; eventually we hope to use spanners to bootstrap multicast over a shared structure. More details on our planne... |

247 |
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- 1981
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Citation Context ...hat the distance between anytwo nodes does not exceed the shortest path distance by amultiplicative factor k. Unlike other commonly-used shared structures, such as Steiner Minimal Tree approximations =-=[16, 13, 9]-=- or core-based trees [1, 7], the k-spanner can bound the path length between any two vertices in the graph. This bound can take into account hop count, Euclidean distance, or link weights. In this pap... |

230 |
Routing Information Protocol
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- 1988
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Citation Context ... may prune themselves o , resulting in a shortest-path multicast tree. DVMRP builds the shortest-path spanning tree by incorporating its own distance-vector unicast routing protocol, a variant of RIP =-=[8]-=-. To reduce this dependence on a particular unicast routing protocol, dense-mode PIM [6] oods the entire network, before pruning from leaf nodes as in DVMRP.sClearly, ooding the network as dense-mode ... |

150 |
Steiner problem in networks: A survey
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126 |
An optimal synchronizer for the hypercube
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- 1987
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Citation Context ...6 we discuss our conclusions and several areas for future research, particularly in applying this work to multicast. 2 Graph Spanners The notion of graph spanners was introduced about a decade ago in =-=[11]-=-. Each spanner is parameterized by a constant k, as follows: A k-spanner of a graph G = (V;E) is a graph S = (V;E 0 ), where E 0 is a subset of E, such that the distance in S between any pair of verti... |

122 | Thetrade-[] of multicast trees and algorithms
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Citation Context ... ratios that compare values of the metrics for a spanner or a spanning tree to the corresponding values for the original graph. This use of ratios to compare graph metrics is similar to that used in [=-=Wei and Estrin 1994-=-] to evaluate options for multicast shared trees. The ratios of the numbers of edges are less than 1.0, while distance-related ratios are greater than 1.0 (reflecting the increased distance due to exc... |

116 |
Core Based Trees
- Ballardie, Francis, et al.
- 2003
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Citation Context ...cribe an experiment that we have conducted to provide some answers to these questions. There are a number of multicast protocols under consideration for use in administrative domains on the Internet [=-=Ballardie et al. 1993-=-; Deering et al. 1996]. All rely upon establishing a distribution tree that covers the receivers of a multicast group. There are two primary ways for characterizing trees used by the protocols. In a p... |

67 |
GT-ITM: Georgia Tech internetwork topology models (software
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Citation Context ...get some indication as to the stability of our results relative to the random number generator used to create the network graphs. We use the suite of random graph generators available at Georgia Tech =-=[5]-=-. These algorithms all place a set of n vertices on a square in the plane, and then consider each pair of vertices in turn, deciding whether an edge is to be added between them. The purely random sche... |

62 |
Mechanisms for Broadcast and Selective Broadcast
- Wall
- 1980
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Citation Context ...hat the distance between anytwo nodes does not exceed the shortest path distance by amultiplicative factor k. Unlike other commonly-used shared structures, such as Steiner Minimal Tree approximations =-=[16, 13, 9]-=- or core-based trees [1, 7], the k-spanner can bound the path length between any two vertices in the graph. This bound can take into account hop count, Euclidean distance, or link weights. In this pap... |

57 | Tree spanners
- Cai, Corneil
- 1995
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Citation Context ...n whether edges of G are weighted or unweighted (i.e., weights all equal to one). Finally, determining whether an arbitrary graph has a k-spanner that is a tree or that is planar is also NP-complete [=-=Cai and Corneil 1995-=-; Brandes and Handke 1998]. Given the apparent intractability of finding minimum-weight spanners, a greedy algorithm that finds relatively light-weight spanners can be used. The algorithm is defined a... |

49 |
Protocol independent multicast version 2 dense mode specification
- Deering, Estrin, et al.
- 1999
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Citation Context ...shortest-path spanning tree by incorporating its own distance-vector unicast routing protocol, a variant of RIP [8]. To reduce this dependence on a particular unicast routing protocol, dense-mode PIM =-=[6]-=- oods the entire network, before pruning from leaf nodes as in DVMRP.sClearly, ooding the network as dense-mode PIM does is expensive, as every edge in the graph is visited at least once by each messa... |

33 |
NP-completeness of minimum spanner problems
- Cai
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Citation Context ...em of deciding whether a k-spanner exists that has total weight (i.e., sum of weights associated with edges) less than W in an arbitrary graph G has been shown to be NP-complete for most values of k [=-=Cai 1994-=-]. The problem remains NP-complete for any planar, biconnected Spanners and Message Distribution in Networks \Delta 3 graph G, with lower limits for k depending on whether edges of G are weighted or u... |

22 | An approximation algorithm for minimum-cost network design
- Mansour, Peleg
- 1994
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Citation Context ...ties of the spanners generated by this algorithm; they are guaranteed to be sparse (with O(n) edges) and light-weight (within O(log n) of the minimum weight of a spanning tree) for a (log n)-spanner. =-=[10]-=-. 3 Broadcast and Multicast over Spanners There are several alternatives for broadcasting in a network. DVMRP bootstraps multicast communication by rst ooding over a shortest-path spanning tree rooted... |

1 |
Np-completeness results for minimum plannar spanners
- Brandes, Handke
- 1998
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Citation Context ...re weighted or unweighted (i.e., weights all equal to one). Finally, determining whether an arbitrary graph has a k-spanner that is a tree or that is planar is also NP-complete [Cai and Corneil 1995; =-=Brandes and Handke 1998-=-]. Given the apparent intractability of finding minimum-weight spanners, a greedy algorithm that finds relatively light-weight spanners can be used. The algorithm is defined as follows: Algorithm Ligh... |

1 |
An approximationalgorithm for minimum--costnetwork design
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Citation Context ...ies of the spanners generated by this algorithm; they are guaranteed to be sparse (with O(n) edges) and light-weight (within O(log n) of the minimum weight of a spanning tree) for a (log n)-spanner. [=-=Mansour and Peleg 1994-=-]. 2. SPANNERS AND MESSAGE DISTRIBUTION How might spanners be employed for message distribution in networks? One potential application is as a virtual topology for broadcasting. Broadcasting is the co... |

1 | An optimal synchronizer for the hypercube - Farley, Proskurowski, et al. - 1987 |