Low degree connectivity of ad-hoc networks via percolation

Consider the following classical problem in ad-hoc networks. Suppose that n devices are distributed uniformly at random in a given region. Each device is allowed to choose its own transmission radius, and two devices can communicate if and only if they are within the transmission radius of each other. The aim is to (quickly) establish a connected network of low average and maximum degree. In this paper we present the first efficient distributed protocols that, in poly-logarithmically many rounds and with high probability, set up a connected network with O(1) average degree and O(log n) maximum degree. Our algorithms are based on the following result, which is a nontrivial consequence of classical percolation theory. Suppose that each device sets up its transmission radius in order to reach the K closest devices. There exists a universal constant K (independent of n) such that, with high probability, there will be a unique giant component (i.e. a connected component of size Θ(n)). Furthermore, all remaining components will be of size O(log2 n). This leads to an efficient distributed probabilistic test for membership in the giant component, which can be used in a second phase to achieve full connectivity.

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Low degree connectivity of ad-hoc networks via percolation

Advances in Applied Probability ◽

10.1239/aap/1275055242 ◽

2010 ◽

Vol 42 (2) ◽

pp. 559-576

Author(s):

Emilio De Santis ◽

Fabrizio Grandoni ◽

Alessandro Panconesi

Keyword(s):

Ad Hoc Networks ◽

Maximum Degree ◽

High Probability ◽

Ad Hoc ◽

Classical Problem ◽

Universal Constant ◽

Giant Component ◽

Second Phase ◽

Connected Network ◽

Hoc Networks

Consider the following classical problem in ad-hoc networks. Suppose that n devices are distributed uniformly at random in a given region. Each device is allowed to choose its own transmission radius, and two devices can communicate if and only if they are within the transmission radius of each other. The aim is to (quickly) establish a connected network of low average and maximum degree. In this paper we present the first efficient distributed protocols that, in poly-logarithmically many rounds and with high probability, set up a connected network with O(1) average degree and O(log n) maximum degree. Our algorithms are based on the following result, which is a nontrivial consequence of classical percolation theory. Suppose that each device sets up its transmission radius in order to reach the K closest devices. There exists a universal constant K (independent of n) such that, with high probability, there will be a unique giant component (i.e. a connected component of size Θ(n)). Furthermore, all remaining components will be of size O(log2n). This leads to an efficient distributed probabilistic test for membership in the giant component, which can be used in a second phase to achieve full connectivity.

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AMIGM: Animal Migration Inspired Group Mobility Model for Mobile Ad hoc Networks

Scalable Computing Practice and Experience ◽

10.12694/scpe.v20i3.1574 ◽

2019 ◽

Vol 20 (3) ◽

pp. 577-590

Author(s):

Jyotsna Verma ◽

Nishtha Kesswani

Keyword(s):

Ad Hoc Networks ◽

Mobile Ad Hoc Networks ◽

Ad Hoc ◽

Mobility Model ◽

Second Phase ◽

Migration Behavior ◽

Group Mobility ◽

Mobile Ad Hoc ◽

Animal Migration ◽

Hoc Networks

The most widespread notion of mobility model is the representation of mobile node’s movement pattern in the wireless ad hoc networks which has a significant impact on the performance of the network protocols. In this paper, we have proposed an Animal Migration Inspired Group Mobility (AMIGM) model for mobile ad hoc networks based on the migration behavior of animals like, insects, flock of birds, schools of fishes, reptiles, amphibians, etc. The propound model tries to overcome the limitations of the existing mobility models, such as temporal dependencies, spatial dependencies, geographical restrictions and migration of nodes between the group of nodes so that it can realistically model the real world application scenarios. The proposed AMIGM model is based on Animal Migration Optimization (AMO) algorithm, in which each group of nodes has two phases namely, Migration phase and Population updating phase. In the first phase, the model simulates the movement of nodes in the group from one position to another by obeying the swarming laws. In the second phase, the model simulates joining and leaving of the nodes in the group during migration. The protocol dependent and independent performance metrics of the proposed model are compared with Random Waypoint Mobility model (RWP) and Reference Point Group Mobility model (RPGM) through ns-2 simulator.

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A prioritized h-out of-k mutual exclusion algorithm with maximum degree of concurrency for mobile ad hoc networks and distributed systems

Proceedings of the 8th International Scientific and Practical Conference of Students, Post-graduates and Young Scientists. Modern Technique and Technologies. MTT'2002 (Cat. No.02EX550) ◽

10.1109/pdcat.2003.1236316 ◽

2004 ◽

Cited By ~ 2

Author(s):

Jehn-Ruey Jiang

Keyword(s):

Distributed Systems ◽

Ad Hoc Networks ◽

Mobile Ad Hoc Networks ◽

Maximum Degree ◽

Ad Hoc ◽

Mutual Exclusion ◽

Mobile Ad Hoc ◽

Hoc Networks ◽

Mutual Exclusion Algorithm

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On the expected maximum degree of Gabriel and Yao graphs

Advances in Applied Probability ◽

10.1239/aap/1261669589 ◽

2009 ◽

Vol 41 (4) ◽

pp. 1123-1140 ◽

Cited By ~ 3

Author(s):

Luc Devroye ◽

Joachim Gudmundsson ◽

Pat Morin

Keyword(s):

Ad Hoc Networks ◽

Wireless Ad Hoc Networks ◽

Maximum Degree ◽

Ad Hoc ◽

Unit Square ◽

Gabriel Graph ◽

Hoc Networks

Motivated by applications of Gabriel graphs and Yao graphs in wireless ad-hoc networks, we show that the maximum degree of a random Gabriel graph or Yao graph defined on n points drawn uniformly at random from a unit square grows as Θ (log n / log log n) in probability.

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