## Geometric Ad-Hoc Routing: Of Theory and Practice (2003)

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### BibTeX

@MISC{Kuhn03geometricad-hoc,

author = {Fabian Kuhn and Roger Wattenhofer and Yan Zhang and Aaron Zollinger},

title = {Geometric Ad-Hoc Routing: Of Theory and Practice},

year = {2003}

}

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### Abstract

All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of ad-hoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly e#cient on practical average-case networks, however is also in theory asymptotically worst-case optimal. On the other hand we are able to drop the formerly necessary assumption that the distance between network nodes may not fall below a constant value, an assumption that cannot be maintained for practical networks. Abandoning this assumption we identify from a theoretical point of view two fundamentamentally di#erent classes of cost metrics for routing in ad-hoc networks.

### Citations

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Citation Context ...e in a given area (also called "geocasting" [16, 22]). Since none of the intermediate nodes is required to maintain routing lists, geometric routing can be considered a lean version of sourc=-=e routing [14]. Our geom-=-etric routing algorithm GOAFR + (pronounced as "gopher-plus") combines---similarly to earlier proposals [4, 6, 15, 20]---two concepts called greedy routing and face routing. In greedy routin... |

1780 | GPSR: greedy perimeter stateless routing for wireless networks
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(Show Context)
Citation Context ...uting lists, geometric routing can be considered a lean version of source routing [14]. Our geometric routing algorithm GOAFR + (pronounced as "gopher-plus") combines---similarly to earlier =-=proposals [4, 6, 15, 20]-=----two concepts called greedy routing and face routing. In greedy routing mode the algorithm forwards the routed message at each network node to the neighbor closest to the destination. Already in sim... |

707 | Routing with guaranteed delivery in ad hoc wireless networks
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(Show Context)
Citation Context ...uting lists, geometric routing can be considered a lean version of source routing [14]. Our geometric routing algorithm GOAFR + (pronounced as "gopher-plus") combines---similarly to earlier =-=proposals [4, 6, 15, 20]-=----two concepts called greedy routing and face routing. In greedy routing mode the algorithm forwards the routed message at each network node to the neighbor closest to the destination. Already in sim... |

434 |
Optimal transmission ranges for randomly distributed packet radio terminals
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Citation Context ...s of geometric routing---suggested over a decade ago---were of purely greedy nature: At each intermediate network node the message to be routed is forwarded to the neighbor closest to the destination =-=[8, 12, 23]. This can however f-=-ail if the message reaches a local minimum with respect to the distance to the destination, that is a node without any "better" neighbors. Also a "least deviation angle" approach (... |

411 | A Survey on Position-Based Routing in Mobile Ad-Hoc Networks
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Citation Context ...oning systems. The same goal could also be achieved by local information exchange with fixed beacon nodes. Similarly the location of the destination could be learned via an overlay (e.g. peer-to-peer =-=[21, 27]) informat-=-ion system. But also a scenario is conceivable, where a message needs to be sent to any node in a given area (also called "geocasting" [16, 22]). Since none of the intermediate nodes is requ... |

349 | Random Walks and Electric Networks
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Citation Context ...tion, the#e509 del introduced in [19], which assumes that the distance between network nodes cannot fall beneath a constant minimum bound. Graphs with this restriction have also been called civilized =-=[7]-=- or #-precision [13] graphs in the literature. We introduce a general notion of a cost metric, defined as a nondecreasing function of the length of the edge over which a message is sent. We show that ... |

294 | Approximation Algorithms for Connected Dominating Sets
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(Show Context)
Citation Context ...rom [19]. Clustering for the means of ad-hoc routing has been proposed by various researchers [5, 18]. A closely related approach is the construction of connected dominating sets as routing backbones =-=[11, 26]-=-. 3 Model and Preliminaries In this paper we assume that network nodes are placed in the Euclidean plane R 2 . In order to represent adhoc networks we adopt the widely used model, where every node has... |

293 | Routing in clustered multihop, mobile wireless networks with fading channel
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Citation Context ...e case performance. In this paper we use a clustering technique in order to drop the#e366 del assumption from [19]. Clustering for the means of ad-hoc routing has been proposed by various researchers =-=[5, 18]-=-. A closely related approach is the construction of connected dominating sets as routing backbones [11, 26]. 3 Model and Preliminaries In this paper we assume that network nodes are placed in the Eucl... |

285 | Compass Routing on Geometric Networks
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Citation Context ...fail if the message reaches a local minimum with respect to the distance to the destination, that is a node without any "better" neighbors. Also a "least deviation angle" approach =-=(Compass Routing in [17]-=-) cannot guarantee message delivery in all cases. The first geometric routing algorithm that does guarantee delivery was Face Routing introduced in [17] (called Compass Routing II there). Face Routing... |

271 |
Routing and addressing problems in large metropolitan-scale internetworks
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(Show Context)
Citation Context ...s of geometric routing---suggested over a decade ago---were of purely greedy nature: At each intermediate network node the message to be routed is forwarded to the neighbor closest to the destination =-=[8, 12, 23]. This can however f-=-ail if the message reaches a local minimum with respect to the distance to the destination, that is a node without any "better" neighbors. Also a "least deviation angle" approach (... |

196 | Worst-case optimal and average-case efficient geometric ad-hoc routing
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- 2003
(Show Context)
Citation Context ...s back to greedy mode. Besides being asymptotically optimal, however, simulations show that in the average case GOAFR+ even outperforms the best (not asymptotically optimal!) algorithms considered in =-=[20]-=-. In particular GOAFR+ consists of the following steps: GOAFR+ The algorithm parameters ae0, ae, and oe are chosen prior to algorithm start and remain constant throughout the execution. For the algori... |

192 |
Transmission range control in multihop packet radio networks
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Citation Context ...s of geometric routing---suggested over a decade ago---were of purely greedy nature: At each intermediate network node the message to be routed is forwarded to the neighbor closest to the destination =-=[8, 12, 23]. This can however f-=-ail if the message reaches a local minimum with respect to the distance to the destination, that is a node without any "better" neighbors. Also a "least deviation angle" approach (... |

185 | GeoCastâ€”Geographic addressing and routing
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(Show Context)
Citation Context ...d be learned via an overlay (e.g. peer-to-peer [21, 27]) information system. But also a scenario is conceivable, where a message needs to be sent to any node in a given area (also called "geocast=-=ing" [16, 22]-=-). Since none of the intermediate nodes is required to maintain routing lists, geometric routing can be considered a lean version of source routing [14]. Our geometric routing algorithm GOAFR + (prono... |

167 | Geometric spanner for routing in mobile networks
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- 2001
(Show Context)
Citation Context ...n on Delaunay triangulations; this is however not applicable to ad-hoc networks, since Delaunay triangulations may contain arbitrarily long edges, whereas transmission ranges are limited. Accordingly =-=[10]-=- proposed local approximation of the Delaunay Graph, however without improving performance bounds for routing. A more detailed overview of geometric routing can be found in [24]. In [19] we proposed A... |

163 | Geocasting in mobile ad hoc networks: Location-based multicast algorithms
- Ko, Vaidya
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(Show Context)
Citation Context ...d be learned via an overlay (e.g. peer-to-peer [21, 27]) information system. But also a scenario is conceivable, where a message needs to be sent to any node in a given area (also called "geocast=-=ing" [16, 22]-=-). Since none of the intermediate nodes is required to maintain routing lists, geometric routing can be considered a lean version of source routing [14]. Our geometric routing algorithm GOAFR + (prono... |

116 | Online routing in triangulations
- Bose, Morin
- 1999
(Show Context)
Citation Context ..., however, none of them outperforms original Face Routing. Yet other geometric routing algorithms have been shown to reach the destination on special planar graphs without any runtime guarantees [2]. =-=[3]-=- proposed an algorithm competitive with the shortest path between source and destination on Delaunay triangulations; this is however not applicable to ad-hoc networks, since Delaunay triangulations ma... |

106 | Asymptotically Optimal Geometric Mobile Ad-Hoc Routing
- Kuhn, Wattenhofer, et al.
- 2002
(Show Context)
Citation Context ...routing algorithms often has to make irritating or far-fetched assumptions, which would hardly ever hold in practice. In this paper we are able to drop one such assumption, the#e509 del introduced in =-=[19]-=-, which assumes that the distance between network nodes cannot fall beneath a constant minimum bound. Graphs with this restriction have also been called civilized [7] or #-precision [13] graphs in the... |

103 | Message-Optimal Connected Dominating Sets in Mobile Ad Hoc Networks
- Alzoubi, Wan, et al.
- 2002
(Show Context)
Citation Context ...ing set of G. Consequently, all nodes of G have at least one neighbor in GBG . The distributed construction of a subgraph of G with properties a) and b) is described in a number of publications (e.g. =-=[1, 9, 25]-=-). As the backbone contains a dominating set of the underlying graph, every regular node (a node not in the backbone) can be associated to one of its dominators. Since this can be regarded as a cluste... |

103 | NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
- Hunt, Marathe, et al.
- 1998
(Show Context)
Citation Context ...introduced in [19], which assumes that the distance between network nodes cannot fall beneath a constant minimum bound. Graphs with this restriction have also been called civilized [7] or #-precision =-=[13]-=- graphs in the literature. We introduce a general notion of a cost metric, defined as a nondecreasing function of the length of the edge over which a message is sent. We show that the behavior of cost... |

98 | Discrete Mobile Centers
- Gao, Guibas, et al.
- 2001
(Show Context)
Citation Context ...ing set of G. Consequently, all nodes of G have at least one neighbor in GBG . The distributed construction of a subgraph of G with properties a) and b) is described in a number of publications (e.g. =-=[1, 9, 25]-=-). As the backbone contains a dominating set of the underlying graph, every regular node (a node not in the backbone) can be associated to one of its dominators. Since this can be regarded as a cluste... |

84 | Internal node and shortcut based routing with guaranteed delivery in wireless networks
- Datta, Stojmenovic, et al.
- 2001
(Show Context)
Citation Context ...uting lists, geometric routing can be considered a lean version of source routing [14]. Our geometric routing algorithm GOAFR + (pronounced as "gopher-plus") combines---similarly to earlier =-=proposals [4, 6, 15, 20]-=----two concepts called greedy routing and face routing. In greedy routing mode the algorithm forwards the routed message at each network node to the neighbor closest to the destination. Already in sim... |

65 | Dominating-Set-Based Routing in Ad Hoc Wireless Networks
- Wu
- 2002
(Show Context)
Citation Context ...rom [19]. Clustering for the means of ad-hoc routing has been proposed by various researchers [5, 18]. A closely related approach is the construction of connected dominating sets as routing backbones =-=[11, 26]-=-. 3 Model and Preliminaries In this paper we assume that network nodes are placed in the Euclidean plane R 2 . In order to represent adhoc networks we adopt the widely used model, where every node has... |

63 | A scalable location management scheme in mobile ad-hoc networks
- Xue, Li, et al.
- 2001
(Show Context)
Citation Context ...oning systems. The same goal could also be achieved by local information exchange with fixed beacon nodes. Similarly the location of the destination could be learned via an overlay (e.g. peer-to-peer =-=[21, 27]) informat-=-ion system. But also a scenario is conceivable, where a message needs to be sent to any node in a given area (also called "geocasting" [16, 22]). Since none of the intermediate nodes is requ... |

47 | Geometric Spanners for Wireless Ad Hoc Networks
- Wang, Li
- 2002
(Show Context)
Citation Context ...ing set of G. Consequently, all nodes of G have at least one neighbor in GBG . The distributed construction of a subgraph of G with properties a) and b) is described in a number of publications (e.g. =-=[1, 9, 25]-=-). As the backbone contains a dominating set of the underlying graph, every regular node (a node not in the backbone) can be associated to one of its dominators. Since this can be regarded as a cluste... |

37 | Online Routing in Convex Subdivisions
- Bose, Brodnik, et al.
- 2000
(Show Context)
Citation Context ... case, however, none of them outperforms original Face Routing. Yet other geometric routing algorithms have been shown to reach the destination on special planar graphs without any runtime guarantees =-=[2]-=-. [3] proposed an algorithm competitive with the shortest path between source and destination on Delaunay triangulations; this is however not applicable to ad-hoc networks, since Delaunay triangulatio... |

37 |
A Cluster-based Approach for Routing in Ad-Hoc Networks
- Krishna, Chatterjee, et al.
- 1995
(Show Context)
Citation Context ...e case performance. In this paper we use a clustering technique in order to drop the#e366 del assumption from [19]. Clustering for the means of ad-hoc routing has been proposed by various researchers =-=[5, 18]-=-. A closely related approach is the construction of connected dominating sets as routing backbones [11, 26]. 3 Model and Preliminaries In this paper we assume that network nodes are placed in the Eucl... |

20 | Routing with Guaranteed Delivery in Geometric and Wireless Networks
- Urrutia
- 2002
(Show Context)
Citation Context ...e limited. Accordingly [10] proposed local approximation of the Delaunay Graph, however without improving performance bounds for routing. A more detailed overview of geometric routing can be found in =-=[24]-=-. In [19] we proposed Adaptive Face Routing AFR. The execution cost of this algorithm---basically enhancing Face Routing by the employment of an ellipse restricting the searchable area---is bounded by... |

2 |
Worst-Case Optimal and Average-Case E#cient Geometric Ad-Hoc Routing
- Kuhn, Wattenhofer, et al.
- 2003
(Show Context)
Citation Context ... back to greedy mode. Besides being asymptotically optimal, however, simulations show that in the average case GOAFR + even outperforms the best (not asymptotically optimal!) algorithms considered in =-=[20]-=-. In particular GOAFR + consists of the following steps: GOAFR + The algorithm parameters # 0 , #, and # are chosen prior to algorithm start and remain constant throughout the execution. For the algor... |