Heuristic Clustering Algorithms in Ad hoc Networks

The clustering allows the geographical region to be covered into small zones in which each zone can be handled with a powerful node called clusterhead. The clusterheads have direct communication link with each of its members whereas the member nodes of a cluster must go through the clusterhead to communicate with each other. Since choosing clusterheads optimally is an NP-hard problem, existing solutions to this problem are based on heuristic (mostly greedy) approaches. In this paper, we present three well-known heuristic clustering algorithms: the Lowest-ID, the Highest-Degree, and the Node-Weight.


I. Introduction
Wireless networks provide support for two types of network topologies: infrastructured and infrastructureless.The cellular networks, as an example for an infrastructured network, have emerged as the most widely used wireless networks that can support mobile users.The limitations of the infrastructure networks initiated the need for wireless networks without fixed infrastructures.Such networks are called mobile multihop radio networks, or ad hoc networks or peer-to-peer networks.These are in contrast to wireless networks that depend on a pre-existing fixed infrastructure of base stations (as in the case of cellular networks) (see Figure 1).In ad hoc networks, there is no such infrastructure and these networks are created dynamically on-the-fly in an

III. Heuristic Clustering Algorithms
There are several heuristics proposed for selecting clusterheads in ad hoc networks.The most well-known ones include: (1) the Highest-Degree heuristic, (2) the Lowest-ID heuristic, and (3) the Node-Weight heuristic.
The Lowest-ID and the Highest-Degree were the two clustering algorithms that were based on the link-cluster architecture.

III-1. The Lowest-ID Heuristic
The Lowest-ID, also as known as identifierbased clustering, was originally proposed by Baker and Ephremides [1,2,8].This heuristic assigns a unique ID to each node and chooses the node with the minimum ID as a clusterhead.Thus, the IDs of the neighbors of the clusterhead will be higher than that of the clusterhead.A node is called a gateway if it lies within the transmission range of two or more clusterheads.Gateway nodes are generally used for routing between clusters.Figure 2 shows nodes 1 and 3 as clusterheads since both hold the lowest node ID in their clusters and node 14 is a gateway node.

Heuristic Clustering Algorithms in Ad hoc Networks
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III-2. The Highest-Degree Heuristic
The Highest-Degree, also known as connectivity-based clustering, was originally proposed by Gerla and Parekh [9,11].Here the degree of a node is computed based on its distance from others.Each node broadcasts its ID to the nodes that are within its transmission range.A node x is considered to be a neighbor of another node y if x lies within the transmission range of y.The node with maximum number of neighbors, that is, maximum degree is chosen as a clusterhead and any tie is broken by the unique node IDs.
The neighbors of a clusterhead become members of that cluster and can no longer participate in the election process.Since no clusterheads are directly linked, only one clusterhead is allowed per cluster.Figure 2 Basagni et al. [4,5] proposed two algorithms, namely the distributed clustering algorithm (DCA) and the distributed mobility-adaptive clustering algorithm (DMAC).In their approach, each node is assigned a weight (a real number >= 0) based on its suitability of being a clusterhead.A node is chosen to be a clusterhead if its weight is highest among all of its neighbors; otherwise, it joins a neighboring clusterhead.The smaller node ID is chosen in case of a tie.The DCA makes an assumption that the network topology does not change during the execution of the algorithm.Thus, it is proven to be useful for ``quasi-static'' networks (when the nodes are either static or move very slowly).The DMAC algorithm, on the other hand, adapts itself to the network topology changes and can therefore be used for any mobile network.

IV. Conclusions and Future Work
In this paper, we have discussed the heuristic clustering algorithms in mobile ad hoc networks.
Clustering is essentially means partitioning the network into different clusters and allows these clusters to communicate with each other in a wireless medium efficiently in order to achieve a connected network for data communication.Each cluster would be managed by a superior node called ``clusterhead'' and the election of these special nodes is similar to leader election algorithms in distributed systems.The heuristic algorithms discussed include the Highest-Degree heuristic, the Lowest-ID heuristic, and the Node-Weight heuristic.

Figure 2 .
Figure 2. Lowest-ID and Highest Degree Heuristics Example.
shows a 15 node example, where nodes 1 and 3 are clusterheads since both have the highest number of neighbors.