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One of the fundamental properties of an ad hoc network is its connectivity. Maintaining connectivity in wireless networks is extremely difficult due to dynamic changing topology of MANETs. There are several techniques to understand the connectivity level for a given network topology. In this paper, we examine the existing methods and discuss the issues and challenges that are still insurmountable in order to enhance the connectivity properties of wireless multi hop networks.

Amobilead hoc network (MANET) is formed by a group of wireless autonomous mobile nodes to create a typical environment for dynamic communication with no fixed infrastructure or administration. They operate in a decentralized and self organizing manner [

The advantage of ad hoc networks is that the mobile devices communicate with each other in a peer-to-peer fashion, establish a self organizing network without the need of any access point or any pre-existing infrastructure. In short, they can be formed in a spontaneous way, that’s why they are known as ad hoc networks. In these networks, each node plays two vital roles: as mobile node and as router to transfer the packets of other nodes. To achieve a fully connected ad hoc network, there must be a multihop path from a node to every other node depending on two topology attributes: radio transmission range and node density. Their combination plays a vital role in node connectivity.

In a cellular network, also known as infrastructure network, the mobile devices remain connected even if there is a wireless link to at least one of the base stations within its communication range. In ad hoc networks, there are no fixed routers; all nodes are capable of movement that can be dynamically connected in an arbitrary manner. Each node acts as router to maintain the connectivity of the entire network. In case the communication gets broken, the connectivity between other nodes also gets destroyed. If the substantiality or spatial density of nodes is too low, the multihop system for communication will not perform well. In this paper, we study and analyze various techniques related to network connectivity along with their impact on the network topology. The organization of the remaining paper is as follows. Section II discusses the importance of connectivity in ad hoc networks. Section III discusses the research works done in the area. Section IV points out the major issues and challenges in ad hoc network connectivity. Finally, the paper is concluded in section V.

Connectivity in ad hoc networks varies because of the continuous movement of the nodes due to their dynamic nature. It is possible that the movement of one or more nodes from one point to another causes the network partitioning. Maintaining connectivity is a challenge due to unstructured nature of the network topology and the frequent occurring of links and nodes failures due to interference, mobility, radio channel effects, and battery limitations [

Node or Device Failure

Critical Points or Weak Points

Link or Edge Failure

Power or Battery Failure

a) Node Failure: The node failure occurs when an intermediate node or device acting as router is not available due to hardware/software failure or the node moves out of the communication range or the network. The situation has been described in

where

In the above equations

After calculating the link expiration time (LET) in all

Links within the network, the highest amount of LET is determined:

The probability of the proper operation of link between node I and node j is obtained by:

where

b) Power Failure: Power failure occurs when the battery of the node is too low, making it unable to serve as router. The situation has been explained in

c) Link Failure: Link failure can occur due to various factors: link obstacle between communication nodes, fading, node mobility and excessive interference.

d) Critical Points: The weak or critical points of a topology are those links and nodes whose failure results in partioning the network into two or more components. For example, the critical node or articulation node is defined as a node that partitions the network due to its failure. The node C in

The problem of node connectivity was very first time discussed by Cheng and Robertazziin 1989 [

In order to prevent failures from partitioning the network and to maintain end-to-end connectivity, researchers recommend the network topology to be K-connected. The K-connectivity refers that the network should have K-disjoint routes between each node pair, which may be edge disjoint or noded is joint. Till now, the main focus has been on to determine the combination of node density and transmission range in order to provide k-node cconnectivity in a specific deployment scenario in homogeneous nodes or non-homogenous nodes in MANETs. However, very few papers [

The work of different authors have been analyzed with their viewpoints on the ad hoc network connectivity along with techniques used and defects in more pristine manner in

a) Mobility Prediction: Mobility prediction of a node is the estimation of its future locations. The definition of location depends on the type of wireless networks. In infrastructure networks location refers to the access points to which mobile terminal is connected. In infrastructureless networks the location refers to geographical coordinates. Its main advantage is to predict the link expiration time to improve the node connectivity and routing performance. Many location prediction methods are discussed in literature [

b) Connectivity Efficiency and Cost Objective: Since in order to deploy static nodes in place of critical nodes in which lack of nodes are felt, deployment cost of static nodes must be considered. While placing such nodes attention must be paid on to maximize the connectivity and to have minimum cost. But to achieve both connectivity efficiency and cost objective while deploying the critical points is a NP-complete problem. Since few authors have attempt this part [

c) Energy Consumption issues: One of the key challenges is to save the limited energy and use it to prolong the network lifetime considering the network connectivity constraints. Since the energy is the most valuable resources in MANETs, its status should continuously be monitored after network deployment. The paper [

Methods | Assumptions | Findings | Drawbacks |
---|---|---|---|

Random Network Model [ | Given Cluster head that form a dominant independent set in the network graph [ | Provides Network connectivity with very high probability [ | Results are of theoretical interest and cannot be apply to real scenarios |

Spatial Poisson Process and Percolation theory [ | Considers mobile stations that are confirmed to a single dimensional line. At a particular instant in time it is assumed that stations spatial positions can be modeled as a one dimensional Poisson process. | Node’s broadcast message percolate, if the nodes are randomly distributed according to homogeneous Poisson point process on an infinitely large area | Work did not consider the actual distance between nodes. |

Packet radio network model [ | Nodes in the network lie in bounded area. The homogeneous Poisson assumption. Each node is able to communicate with any other node that is at most R unit distance from it. All nodes generate Poisson streams of traffic at an identical rate. | No optimal number of nearest neighbor or magic number can exist. | Difficult to apply in real scenario. Also in disk based models, fading, interference and attenuation does not considerer. |

Connectivity of radio networks [ | Transmitters are distributed according to one dimensional Poisson process of density d. Two transmitters are connected by an edge apart at most i distance of their communication range. | Solve s the problem of [ | Difficult to be apply in real scenario, only the expected number of deployed nodes can be controlled |

Critical power for asymptotic connectivity in wireless networks [ | Nodes placed randomly in disc of unit area. | Estimates the critical power of a node, needed to transmit to ensure that the network connectivity. | Not applicable for real applications. |

Connectivity in ad hoc and hybrid networks [ | Assumes a large scale wireless network with low density of nodes per unit area. Power constraints are modeled by a maximum distance above which two nodes are not directly connected. | Base stations significantly help in increasing the network connectivity only for large density | Findings restricted only to one dimensional case. |

Number of neighbors needed for connectivity of wireless networks [ | In a network with n randomly placed nodes each node should be connected to Ө (log n) neighbors. N nodes are placed uniformly and independently in unit square region. Critical constant appear to be close to 1. | Increasing number of nodes should not effect the number of nearest neighbor otherwise once obtained a disconnected network Asymptotic connectivity results when every node is connected to its nearest 5.1774logn neighbors, while asymptotic disconnectivity results when each node is connected to less then 0.074logn nearest neighbors. | Result is of theoretical interest and cannot be applicable to real scenario |

Approximation algorithms and Connectivity Augmentation Problem [ | Network is treated as undirected graph [ | Determines a set of edges of minimum weight to be inserted so that so that the resulting graph is λ-vertex (edge) connected. The problem is NP hard for λ > 1 | Does not consider the possibility of adding new vertices into the graph |

A probabilistic analysis for the radio range assignment problem in ad hoc networks [ | N nodes having same transmission range are distributed in d-dimensional region. | Estimates bounds for isolated nodes and connected nodes on a one dimensional line segment. | It is only for static networks. It does not incorporate the possibility of transient or permanent node failures in their model. That will lead to requirements for desirable topological characteristic to be harsher compared to theoretical prediction |

Phase transition [ | n nodes located randomly in some service area, each assumed to transmit with a fixed radio power in an idealized environment where it can be heard by other nodes within same radius. | Discusses the theory of Bernoulli random graphs [ | Classical theory of random graph models is not suitable to model the ad hoc network problems. |
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Minimum node degree and connectivity of wireless multi hop network [ | 1. Random uniform distribution of nodes and a simple link model 2. All nodes are free to move in the system area according to a certain mobility model 3. Radio link model is assumed | Finds the uniform distribution of homogeneous nodes in a rectangular deployment area and establishes a relationship between the minimum transmission range and the probabilistic behavior of minimum node degree | Results are of theoretical interest and require a very high node density to ensure k-connectivity which would lead to interference and low throughput in real networks |

Minimum node degree and k-connectivity of a wireless multi hop network in bounded area [ | Circumvent the border effect which assumes boundless network deployment area. | Eliminate the border effects in order to provide an improved estimation of probabilistic characteristic, including the upper bound and lower bound of minimum node degree and k-connectivity. | High node density would lead to interference and low throughput in real networks |

Torus Convention [ | Nodes are distributed on a unit square according to a homogeneous Poisson point process with density λ. | Eliminate the need to consider boundary effects that may affect the critical transmission range for k-connectivity | It is of theoretical interest, requiring a very high node density to ensure k-connectivity which would lead to interference and low throughput in real networks. |

Critical transmitting range for connectivity in sparse wireless ad hoc networks [ | Nnodes, each capable of communicating with nodes within a radius of r, randomly and uniformly distributed in d?dimensional region of side of length l. Consider both stationary and mobile nodes | Estimates tolerating parseness i.e. Requiring 90% of nodes to be in the same connected component results in the significant reduction in the required transmission ranges of nodes. | If physical node degree is upper bounded by a constant, then the resulting communication graph is disconnected |

Connectivity in finite ad hoc networks [ | Uniform distribution of nodes in [0,z] where z > 0 for one dimensional network | Finds the probability of connectivity of one dimensional finite ad hoc network formed by uniform distribution of nodes | Probability of network was not correct and has been corrected by [ |

Cell extension and Mobility patterns [ | All relay nodes are randomly distributed and fixed. Mobile nodes and relay nodes move right at same velocity. Relay nodes are classified into two groups. In first group both relay nodes never move and in other group relay nodes move left at velocity | Finds that multi-hop networking with two kind of mobile relay nodes degrades cell extension performance compared with fixed relay nodes. | It is of theoretical interest and cannot be apply to real scenarios. Also, Distributions of mobile nodes are considered only on street not on plane. |

Asymptotic critical transmission radius and critical neighbor number for k-connectivity [ | Uniform n point process over a unit area disk or square. | Obtained the improved asymptotic almost sure upper bound on the critical neighbor number for k-connectivity. | It does not consider interference, though dense networks produce strong interference. Decrease the network throughput. |

Geometric random graph theory [ | Number of nodes placed in uniformly distributed area. Homogeneous topology control | Asymptotic distribution to analyze the critical transmission range | It can only be used to model dense ad hoc networks, not for sparse ad hoc networks [ |
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Centralized topology control algorithm [ | Relative distance of all nodes are given as input to a centralized topology control algorithm | Minimize the maximum transmitting range of nodes. Also, reduce the energy consumption and improve the network throughput | No information has been given to select the appropriate number of neighbors for LINT heuristic (Local Information No Topology). Danger of Network partition in LINT. |

Distributed position based network protocol [ | Every node is equipped with a GPS receiver. Also, The number of iteration needed to determine the enclosure is based on the definition of the initial search engine | Minimizes the energy needed to communicate with a single master node. | The search engine is a critical aspect which affects the energy consumption of the protocol. |

Cone-based distributed topology control algorithm [ | Each node has some power function which transmits the minimum power needed to establish a communication link to a node far away from that node. | Reduce the power consumption and discuss the modification to deal with mobility. | Initial range assignment for nodes and its step increase has not been discussed. |

Depth first search algorithm [ | Nodes know their location and periodically update their neighbors with their current locations. | Determine the critical links whose failure cause partitioning of the network and then supporting these links either by modifying the trajectory of the nodes involved in the critical links or bringing an outside node to reinforce them. | Increase delivery rates due to Prolonged network connectivity. Communication overhead due to running DFS (Depth First Search) for detecting critical links was not measured. |

Localized algorithm for testing k-connectivity [ | Each node makes its own decision based on the information available in its local neighborhood. Each node verifies whether or not itself and each of its p-hop neighbors of a given node is k-connected. All nodes declare themselves locally 1-connected. | Find the critical nodes and links using local topology and location information | Detected critical points may not be global critical points due to existence of alternate routes |

Genetic Algorithm and Fish Swarm Algorithm [ | Realistic Mobility Model | Improve the node connectivity issue by adding static nodes with consideration to deployment cost | Energy loss while deploying static nodes is not considered |

Linear Programming and Neural Networks [ | Consider a network of homogeneous and energy constrained sensor nodes that are randomly deployed in a sensor field. | scheme is quite effective to deliver 95% of packets to their destination with increase in network coverage | It cannot guarantee the full sensing coverage of the network. |

Fractal Propagation Model [ | For every two nodes within the transmission range will be connected with a probability as function of their geometrical distance. | Giant component size can be characterized by a single parameter i.e. average node degree. | Giant component size has been estimated empirically rather than analytically |

Undirected Geometric Random Graph [ | n nodes are randomly and uniformly distributed on a square and link exist between two nodes if the power received at one node from the other nodes is greater then a given threshold. | It shows an empirical formula relating the giant component size and the average node degree in random geometric graphs. | Giant component size of network has been estimated empirically rather then analytically. |

In this paper, we have reviewed the existing literature with respect to network connectivity. The network connectivity is an important property of ad hoc network because the mobile nodes change the network topology very frequently. If the network becomes disconnected, the data may not be sent to the desired destination. Most of the existing works have considered unrealistic scenarios and very less works discuss the major factors contributing to network disconnectivity in MANETs. We have highlighted important parameters that affect the network connectivity, which include battery/power failure, link failure, critical points, and node failure. The main issues in network connectivity are mobility prediction, energy consumption and connectivity efficiency along with connectivity cost and these issues need to be explored further to understand network connectivity.

MohitJain,SatishChand, (2016) Issues and Challenges in Node Connectivity in Mobile Ad Hoc Networks: A Holistic Review. Wireless Engineering and Technology,07,24-35. doi: 10.4236/wet.2016.71003