Geographic routing without location information

Rao, Ananth; Ratnasamy, Sylvia; Papadimitriou, Christos H.; Shenker, Scott; Stoica, Ion

doi:10.1145/938985.938996

Cited by 508 publications

(355 citation statements)

References 24 publications

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“…All earlier papers assumed that vertices are aware of their physical location, an assumption which is often violated in practice for various of reasons (see [16,28,35]). In addition, implementations of recovery schemes are either based on non-rigorous heuristics or on complicated planarization procedures.…”

Section: Some Known Strategiesmentioning

confidence: 99%

“…In addition, implementations of recovery schemes are either based on non-rigorous heuristics or on complicated planarization procedures. To overcome these shortcomings, recent papers [16,28,35] propose routing algorithms which assign virtual coordinates to vertices in a metric space X and forward messages using geographic routing in X. In [35], the metric space is the Euclidean plane, and virtual coordinates are assigned using a distributed version of Tutte's "rubber band" algorithm for finding convex embeddings of graphs.…”

Section: Some Known Strategiesmentioning

confidence: 99%

“…To overcome these shortcomings, recent papers [16,28,35] propose routing algorithms which assign virtual coordinates to vertices in a metric space X and forward messages using geographic routing in X. In [35], the metric space is the Euclidean plane, and virtual coordinates are assigned using a distributed version of Tutte's "rubber band" algorithm for finding convex embeddings of graphs. In [16], the graph is embedded in R d for some value of d much smaller than the network size, by identifying d beacon vertices and representing each vertex by the vector of distances to those beacons.…”

Section: Some Known Strategiesmentioning

confidence: 99%

“…The distance function on R d used in [16] is a modification of the 1 norm. Both [16] and [35] provide substantial experimental support for the efficacy of their proposed embedding techniquesboth algorithms are successful in finding a route from the source to the destination more than 95% of the time -but neither of them has a provable guarantee. Unlike embeddings of [16] and [35], the embedding of [28] guarantees that the geographic routing will always be successful in finding a route to the destination, if such a route exists.…”

Section: Some Known Strategiesmentioning

confidence: 99%

See 3 more Smart Citations

Navigating in a Graph by Aid of Its Spanning Tree

Dragan

Matamala

2008

Algorithms and Computation

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Abstract. Let G = (V, E) be a graph and T be a spanning tree of G. We consider the following strategy in advancing in G from a vertex x towards a target vertex y: from a current vertex z (initially, z = x), unless z = y, go to a neighbor of z in G that is closest to y in T (breaking ties arbitrarily). In this strategy, each vertex has full knowledge of its neighborhood in G and can use the distances in T to navigate in G. Thus, additionally to standard local information (the neighborhood NG(v)), the only global information that is available to each vertex v is the topology of the spanning tree T (in fact, v can know only a very small piece of information about T and still be able to infer from it the necessary tree-distances). For each source vertex x and target vertex y, this way, a path, called a greedy routing path, is produced. Denote by gG,T (x, y) the length of a longest greedy routing path that can be produced for x and y using this strategy and T . We say that a spanning tree T of a graph G is an additive r-carcass for G if gG,T (x, y) ≤ dG(x, y) + r for each ordered pair x, y ∈ V . In this paper, we investigate the problem, given a graph family F, whether a small integer r exists such that any graph G ∈ F admits an additive r-carcass. We show that rectilinear p × q grids, hypercubes, distance-hereditary graphs, dually chordal graphs (and, therefore, strongly chordal graphs and interval graphs), all admit additive 0-carcasses. Furthermore, every chordal graph G admits an additive (ω(G) + 1)-carcass (where ω(G) is the size of a maximum clique of G), each 3-sun-free chordal graph admits an additive 2-carcass, each chordal bipartite graph admits an additive 4-carcass. In particular, any k-tree admits an additive (k +2)-carcass. All those carcasses are easy to construct.

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Section: Some Known Strategiesmentioning

confidence: 99%

Section: Some Known Strategiesmentioning

confidence: 99%

Section: Some Known Strategiesmentioning

confidence: 99%

Section: Some Known Strategiesmentioning

confidence: 99%

See 2 more Smart Citations

Navigating in a Graph by Aid of Its Spanning Tree

Dragan

Matamala

2008

Algorithms and Computation

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“…The advancement of technologies in GPS and relative coordinate positioning systems using signal strength or topology information [8,9] show the feasibility of applying geographic information in routing decisions. In this paper, we assume some location service system is available, for example, [10,11].…”

mentioning

confidence: 99%

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

Yi¹,

Wan²,

Su³

et al. 2010

The Computer Journal

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In grid routing, the plane is tessellated into equal-sized square cells. Two cells are called neighbor cells if they share a common edge, and two nodes are called routing neighbors if they are in neighbor cells and within each other's transmission range. If communication parties are in the same cell, packets can be transmitted directly; otherwise, packets are forwarded to routing neighbors that are in cells closer to destination cells. As a greedy strategy, grid routing suffers the existence of local minima at which no neighbor nodes exist for relaying packets. To guarantee deliverability, in this paper, we investigate two vital parameters of grid routing, called the grid size and the transmission radius. Assume that nodes are represented by a Poisson point process with rate n over a unit-area square, and let l denote the grid size and r the transmission radius. First, we show that if l = β ln n/n for some constant β and r = √ 5l, then β = 1 is the threshold for deliverability. In other words, there almost surely do not exist local minima if β > 1 and there almost surely exist local minima if β < 1. Next, for any given β > 1, we give sufficient and necessary conditions to determine the critical transmission radius (CTR) for deliverability. Then, we show that as β ∼ = 1.092, the CTR r ∼ = 2.09 √ ln n/n is the minimum over all β > 1. Simulation results are given to validate this theoretical work.

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Location Discovery in Sensor Networks

Nasipuri

2008

Algorithms and Protocols for Wireless Sensor Networks

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Geographic routing without location information

Cited by 508 publications

References 24 publications

Navigating in a Graph by Aid of Its Spanning Tree

Navigating in a Graph by Aid of Its Spanning Tree

The Critical Grid Size and Transmission Radius for Local-Minimum-Free Grid Routing in Wireless Ad Hoc and Sensor Networks

Location Discovery in Sensor Networks

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