The Number of Neighbors Needed for Connectivity of Wireless Networks

By F. Xue, P. Arun Raj Kumar. Wirel. Networks, 2004

898 citations recorded by the source corpus.

Subfields: Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/91d5e39c5ab9642495f511c15d17c3a20967c46e

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In Computer Networks and Communications

Citations in the corpus

Constrained coverage for mobile sensor networks (2004, background): “2) Evidence from the theory of random networks indicates that global network connectivity is strongly dependent on node degree [3], a local constraint.”
The Complexity of Connectivity in Wireless Networks (2006, neutral): “[31], [8].”
Network coverage using low duty-cycled sensors: random & coordinated sleep algorithms (2004, background): “Conditions for asymptotic connectivity for a general network were derived in [4].”
Coverage and hole-detection in sensor networks via homology (2005, background): “Other approaches [6], [7], [8] give percolationtype results about coverage and network integrity for randomly distributed nodes.”
Batch Informed Trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs (2014, background): “Common RGGs have edges to a specific number of each state’s nearest neighbours (a k-nearest graph [35]) or to all neighbours within a specific distance (an r-disc graph [36]).”
Computing and communicating functions over sensor networks (2005, background): “1 in [7], limn→∞ Pr[Some square has more than C log n nodes] = 0, for some constant C > 0.”
Agreement over random networks (2004, background): “We note that in some situations the basic assumption hidden in the random graph model should be relaxed with more appropriate probabilistic models such as those offered by random geometric graphs [22], [25].”
Principles and protocols for power control in wireless ad hoc networks (2005, neutral): “9) The choices of power levels affect the connectivity of the network (see [1] and [2]), and consequently, the ability to deliver a packet to its destination.”
ATPC: adaptive transmission power control for wireless sensor networks (2006, background): “These works can be classified in three major categories according to the transmission range and power assumptions: network-level uniform transmissio n power [27] [25] [2] [18] [31], node-level non-uniform trans mission power [11] [2] [18] [19] [28] [37] [17] [26] [30] [22] , and neighbor-level trans”
Robomote: enabling mobility in sensor networks (2005, background): “This is logical since network connectivity might not exist for networks below node degree 6 [ Xue and Kumar 2003 ].”
Impact of interferences on connectivity in ad hoc networks (2005, background): “powers of the nodes are different in [7].”
Coverage in sensor networks via persistent homology (2007, methodology): “Such methods are more appropriate in contexts for which the coordinates of nodes are unknown, see [13, 19, 15]; however, the assumptions on the uniformity of the distribution are crucial.”
A Survey of Fault Management in Wireless Sensor Networks (2007, neutral): “Authors in [15] explore the problem of the number of one-hop neighbors per node necessary for the network connectivity as a function of the network size.”
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms (2009, methodology): “Using the k-nearestneighbor graph over uniformly placed nodes, the analysis in [Xue and Kumar, 2004] suggests that the minimal number of neighbors in a connected network grows with log(n).”