Critical Power for Asymptotic Connectivity in Wireless Networks

Gupta, Piyush; Kumar, P. R.

doi:10.1007/978-1-4612-1784-8_33

Cited by 780 publications

(800 citation statements)

References 7 publications

Supporting

Mentioning

786

Contrasting

Order By: Relevance

“…In a 2-dimensional random geometric graph, n nodes are randomly assigned coordinates uniformly in unit square, and two nodes are connected with an edge when their Euclidean distance is less than or equal to a connectivity radius, r [6,7]. In [6] it is shown that if the connectivity radius scales as r con (n) = Θ( log n n ) then the network is connected with high probability. Throughout this paper when we refer to a random geometric graph, we mean one with the connectivity r con (n).…”

Section: Previous Work and Known Resultsmentioning

confidence: 99%

Fast Decentralized Averaging via Multi-scale Gossip

Tsianos¹,

Rabbat²

2010

Distributed Computing in Sensor Systems

View full text Add to dashboard Cite

Abstract. We are interested in the problem of computing the average consensus in a distributed fashion on random geometric graphs. We describe a new algorithm called Multi-scale Gossip which employs a hierarchical decomposition of the graph to partition the computation into tractable sub-problems. Using only pairwise messages of fixed size that travel at most O(n 1 3 ) hops, our algorithm is robust and has communication cost of O(n log log n log −1 ) transmissions, which is order-optimal up to the logarithmic factor in n. Simulated experiments verify the good expected performance on graphs of many thousands of nodes.

show abstract

Section: Previous Work and Known Resultsmentioning

confidence: 99%

Fast Decentralized Averaging via Multi-scale Gossip

Tsianos¹,

Rabbat²

2010

Distributed Computing in Sensor Systems

View full text Add to dashboard Cite

show abstract

“…Random geometric graphs are often used to model the one-hop connectivity in wireless networks, where the threshold γ can be viewed as a proxy to the communication range employed by wireless nodes; e.g., [27,33,34].…”

Section: Random Geometric Graphsmentioning

confidence: 99%

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

Kabkab

2015

Internet Mathematics

View full text Add to dashboard Cite

We introduce a new random graph model. In our model, n, n ≥ 2, vertices choose a subset of potential edges by considering the (estimated) benefits or utilities of the edges. More precisely, each vertex selects k, k ≥ 1, incident edges it wishes to set up, and an undirected edge between two vertices is present in the graph if and only if both of the end vertices choose the edge. First, we examine the scaling law of the smallest k needed for graph connectivity with increasing n and prove that it is (log(n)). Second, we study the diameter of the random graph and demonstrate that, under certain conditions on k, the diameter is close to log(n)/ log(log(n)) with high probability. In addition, as a byproduct of our findings, we show that, for all sufficiently large n, if k > β log(n), where β ≈ 2.4626, there exists a connected Erdös-Rényi random graph that is embedded in our random graph, with high probability.

show abstract

“…Reasonably, in the case R = 22m, a higher node density is required to reach this reachability. Detailed studies of critical density for wireless network connectivity can be found in [20], [21]. Here, we will focus on the comparison among different k-hop searching results.…”

Section: A Study Of Simple Geographic Greedy Routingmentioning

confidence: 99%

An exploration of geographic routing with k-hop based searching in wireless sensor networks

Chen

Song

2008

2008 Third International Conference on Communications and Networking in China

View full text Add to dashboard Cite

Abstract-We explore the asymptotic performance of existing geographic routing with a utilization of k-hop neighborhood information. The reachability from source to sink improves as we use more information for routing decision and the average number of hops required decreases significantly from 1-hop to 2-hop searching, which indicates a potential tradeoff between performance enhancement and system complexity. As simple greedy geographic routing is insufficient in lossy wireless environment, we propose a new metric incorporating both advance in distance and link quality. Through simulations, we show its effectiveness over the conventional simple greedy method. The generalization to k-hop based routing and resulting performance are also presented. Simulation results show that with the multi-hop based searching, there is a good improvement in the number of transmissions required from source to sink, which also indicates potential improvement in routing delay and energy consumption in transmissions.

show abstract

Critical Power for Asymptotic Connectivity in Wireless Networks

Cited by 780 publications

References 7 publications

Fast Decentralized Averaging via Multi-scale Gossip

Fast Decentralized Averaging via Multi-scale Gossip

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

An exploration of geographic routing with k-hop based searching in wireless sensor networks

Contact Info

Product

Resources

About